Info on compatibility and mixed fan systems is needed here to clarify.
The speed of an older 3-pin fan is controlled ONLY by varying the VOLTAGE supplied to it. The header pinout is: Pin 1 (Black) GROUND, Pin 2 (Red) + VDC, Pin 3 (Yellow) Speed Signal. The VOLTAGE on Pin 2 can vary form 12 VDC (full speed) to 5 VDC (the lowest it can go without risking stalling the fan). The speed signal is generated inside the fan motor as a series of 5 VDC pulses (2 per revolution) sent back to the fan header on Pin 3 for counting and display. This speed signal is NOT used for control of speed, but most fan headers DO monitor it for FAILURE, and will pop up a warning on your screen if that happens. (SOME CPU_FAN headers will take more drastic action quickly to prevent possible overheating of an uncooled CPU chip resulting in expensive damage.)
The newer 4-pin PWM fans have a different design and signals, but some are the same because they were designed for maximum backwards compatibility. Pin #1 (Black) is GROUND, Pin 2 (Yellow) is +12 VDC (constant), Pin 3 (Green) is Speed signal, Pin 4 (Blue) is PWM signal. (There is one other colour coding sytem used in fewer fans.) Pins 1 and 3 are unchanged. Pin 2 has the full 12 VDC power supply at all times. Pin 4 carries the new PWM signal to the fan. Note that the similarity of electrical signals and pin uses AND the physical pin layout makes it possible to plug either type of fan into either type of mobo header. A Pulse Width Modualtion signal is a lot like a "Square Wave" because it is either fully on or fully off. But whereas a Square Wave is "on" exactly 50% of the time always, a PWM signal varies the "% On" value from 0 to 100 %. In computer PWM fans, the signal is 5 VDC amplitude at a frequency of 20 to 22 kHz. PWM fan motors include inside a small chip that uses thie PWM signal to modify (Switch) the power from the fixed 12 VDC source (Pin 2) though the motor windings to deliver changes in average torque force to accomplish speed control.
It has become VERY common that all mobo fan headers now have 4 pins, but the mobo headers' design allows it to use those as either a 3-pin older Voltage Control Mode (aka DC Mode) system OR as a new 4-pin PWM Mode system. If the fan you plug in matches the type of signal being sent to it, all fans work as expected and their speeds are controlled. Mismatches give slightly different results. If a new PWM fan is plugged into a header using the older Voltage Control Mode, it gets NO PWM signal to use so it cannot change the power to the windings that way. However, the Voltage being supplied on Pin #2 in this Mode can be REDUCED to reduce motor speed, so its speed still IS controlled by the header. On the other hand, if you plug a 3-pin fan into a header using the new PWM Mode for control, that fan does NOT make any connection to the PWM signal on Pin #4, and does not have the special chip inside to use that signal, anyway. It receives from Pin #2 the constant 12 VDC power supply, so it always runs full speed. You get good cooling (maybe too much) but no control of speed in this mismatch.
A SPLITTER used to connect two or more fans to a single header merely connects all its fans in parallel to the signals from the header, so each fan gets whatever that is. This also means that the group of fans is limited by the capacity of the header to supply current on Pins 1 and 2, typically max 1.0 A total load for each header. So in using a Splitter one MUST verify the max current draw from each fan on the Splitter and ensure that load limit is not exceeded. A HUB does it differently. The Hub has an extra connecting a "arm" to a PSU output, and all of the power supplied to all of the fans on Pins 1 and 2 comes from the PSU, and NOT from the mobo header, so that current limit is avoided. (There is a larger current limit due to the connectors in the lines from the PSU, but that is rarely a problem.) The Hub DOES distribute to all its fans the PWM signal from the header (this does not present an electrical load problem) and does return to the header the speed of one fan.
NOTE that the common HUB design REQUIRES a PWM signal from the mobo header to work, and can control its fans speeds ONLY by distributing to them that PWM signal. The power supply lines provide only fixed 12 VDC and Ground connections. So a Hub can ONLY control the speed of the new 4-pin PWM fans. (There are one or two exceptions to that in particular Hubs of different design.) In general, to connect several older 3-pin fans to a header and control their speeds that way, you MUST use a SPLITTER and connect that to a header configured to use the older Voltage Control Mode.
A mobo header determines the speed of its fan by counting the pulses returned to it on Pin #3. But it cannot deal with multiple streams of pulses from more than one fan. So any Splitter or Hub will send back the speed signal from only ONE of its fans, and the other fans' speed signals simply are ignored. They will never be seen anywhere. One way to do this is just to omit Pin #3 in most of the output ports, and include that pin in only one port. Splitters and Hubs without that design typically will label the one port that DOES return its speed signal, sometimes as the "CPU Fan" port. So one fan always should be plugged into that output port to send a speed signal to the mobo header.
OP, back to your specific system, knowing now the AIO details. You are correct about the proper connections.
The RAD FANS should be connected to the CPU_FAN header so their speeds can be controlled automatically according to the temperature reported by a sensor built into the CPU chip itself. You can use your FH-04 Splitter unit for that (IF it is working properly - see below.) Go into BIOS Setup for that header. Look closely at the header configuration for these details. It should be set to use PWM Mode for the electrical characteristics of your fans. That is the METHOD by which the header can implement the speed it has chosen for your fans. Now check the Profile setting - a setting with choices like: "Normal" or "Automatic" or "Standard"; Turbo or Full; Quiet; or some fixed speed you set manually. This is the STRATEGY for how the system decides what speed the pump should be running. Sometimes an option is called "Manual", but really is a way for YOU to set the "fan curve" of speed versus temperature as a replacement for the default fan curve used by the "Standard" Profile. That option still will constantly change the fans' speeds according to CPU temperature, just slightly different from the default strategy. I suggest you set to "Standard", the default automatic control system, for now.
The PUMP should be plugged into the mobo PUMP header. That header is normally configured to supply power ONLY at the full 12 VDC level so that it always runs full speed. BUT some mobos allow you NOT to use the header that way, and use it just like any other header. You have not told us what mobo you have, so we cannot examine its manual for details. Now, SOME pumps are designed like older 3-pin fans and will run full speed all the time if connected to a header using the new PWM Mode. BUT the system you have says its pump is designed like a 4-pin PWM fan so you have the option to run it slower speeds, depending on how the header is configured. In general this is not a good method. In controlling the CPU cooling if the system tries to change the speeds of BOTH the PUMP and the RAD FANS, those two sources of cooling "chase each other around" resulting in big swings in CPU temperature. The very common practice is to keep the pump at a fixed speed (usually full speed) and let ALL control of the CPU temperature be done solely by altering the speed of the RAD FANS. But you CAN make use of your system features in this way: you can set a fixed pump speed in the header for that unit (rather than using an automatic Profile setting). YOU can decide whether your workload is very high, requiring maximum circulation of liquid so the fans can do their job without maxing out their speed. OR perhaps your workload is lighter and the fans are loafing along at minimum speed. In that case you could set a slower fixed speed for the pump and let the fans work just a little harder. You do not need to make such pump speed changes often.
So, IF your pump is connected to the PUMP header, go into BIOS Setup to that header. Check whether the options include a choice for the intended use of this header - some mobos allow you to choose to have it be a PUMP header or a FAN header. IF you have that, set it for FAN use IF you want to be able to alter the fixed pump speed manually. In the Profile setting field do not use the version of this often labelled "Manual" that really is an alternative FAN CURVE setting. That would simply change your pump speeds according to a different Fan Curve. Choose some fixed pump speed - maybe full speed for now, and you can re-examine this later. When you have your settings to your liking, remember to use ESC to return to the Main Menu, then F10 to get to an Exit Menu. There choose to SAVE Settings and EXIT to reboot with the new settings.
Now, with those configuration settings confirmed, re-examine whether your rad fans are all running full speed all the time, as before. If they now are under speed control and reducing speed when the system is cool, you have it fixed. If they still are running full speed always there are three possible causes. One is the AIO system is not circulating fluid fast enough. You have not reported any symptoms indicating that failure, but it's a possibility to remember for later. Another is that the CPU_FAN header for whatever reason is not sending out a PWM signal, so the rad fans are running full speed to guarantee cooling with no control. Another is that the FH-04 unit is faulty and is failing to pass that PWM signal on to all its fans. That is why I suggested the test of plugging the RAD FAN Splitter into another mobo header. Now, there's a caution for this test. If you do that, the CPU_FAN header will get NO fan speed signal back, and will go into alarm mode and may shut you down! So, with the system off, move the SPLITTER input cable from the CPU_FAN header to a mobo SYS_FAN header. Then move one of your case vent fan's cables to the CPU_FAN header so that both headers still will get valid fan speed signals and NOT panic. Boot up and observe the rad fans on the FH-04 unit. If they still run full speed all the time, then it is VERY likely that unit is faulty and you need to contact their Tech Support people for a replacement under warranty. BUT if those fans DO run at controlled lower speeds this way but do NOT when the FH-04 is plugged into the CPU_FAN header, then there is a problem with that header.
Post back here what you find out.