I'll offer different advice, and explain.
There really are three types of cables to connect. Both rad fans and the pump unit have standard fan connectors on them with little ridges running down their sides. The system comes with a fan Splitter so you can connect both rad fans to a single mobo fan header. Then each fan has a second cable ending in a wider 4-hole plain RGB connector for the LIGHTS in their frames, and there is a lighting Splitter so you can connect them to the little manual 3-button Controller. NOTE that for these lighting connections, each connector has a small triangle marking the +12 VDC line, and those MUST be aligned with a matching mark on the mating male connector.
All mobo fan headers do an important secondary function. They monitor the speed signal of the fan connected to them, and warn you if that signal is missing, indicating fan FAILURE. For the CPU_FAN header, many mobos do more that that - if the fan fails, it may actually shut down your system even before the temperature inside the CPU chip goes too high, anticipating that overheating WILL happen if there is no cooling. Now, when using an AIO system, the most important component to monitor for failure is the PUMP. If it is working but one or both rad fans fail, the temperaure of the CPU will rise slowly, and that will cause the system to throttle back and then shut down more slowly. But if the PUMP fails, there is no movement of heat to the rad, and the CPU can overheat rapidly. So, the PUMP should be plugged into the CPU_FAN header so its speed signal can be monitored closely. The RAD FANS should be connected to the CPU_OPT header, which will control the fan speeds according to the internal CPU chip temperature.
The PUMP unit does require a constant full 12 VDC power supply to run full speed all the time. The design of this system takes advantage of an odd quirk of the difference between 3-pin and 4-pin fans. A 4-pin fan header operating in PWM Mode supplies constant 12 VDC power to its fan, plus a PWM control signal that the fan itself uses to adjust its speed. If you plug a 3-pin fan into such a header, that fan has no way to use the PWM signal, so it always runs full speed. In your AIO system, the PUMP is wired just like a 3-pin fan, so connecting it to the CPU_FAN header and ensuring that header does use the new PWM Mode will guarantee that the pump always runs full speed.
When your system is connected and operating, go into BIOS Setup to the place where you can configure the fan headers - see your mobo manual, p. 3-40. For BOTH the CPU_FAN and CPU_OPT headers, configure as:
Q-FAN Control to Auto - the manual says this will put the header into the newer PWM Mode, suitable for the 4-pin rad fans and just what the Pump unit needs
CPU Fan Profile Standard so the mobo will do automatic control of the cooling system as pre-programmed
Now to the lighting cables. You have a Splitter to connect both fans' lighting cables together to the small manual controller box. Then there's another cable to connect a power supply line from the PSU to that Controller. With that you control the light displays by the buttons on the Controller. What the manual does not discuss is that the lights CAN be controlled instead by a mobo plain RGB header IF you have one. You have not told us what mobo you have, so I can't check that detail. That header would have FOUR pins, not three. If you have that, you do not need the manual Controller box and its power connection. You can just plug the lighting Splitter into the mobo 4-pin RGB header and use the software utility that comes with your mobo to control the lights.