Some confusing and wrong info above.
First, any RGB fan has TWO cables from it. One ends in a standard female fan connector with either 3 holes or 4 in it - depends on the fan motor type. This is for the MOTOR of the fan. Then it has a separate cable much wider that ends on a 4-pin connector, OR a 3-pin connector like the 4-pin but with one pin missing. THIS is for the RGB lights in the fan frame only, and it is normally a FEMALE connector also (with holes). How many wires and pins are part of the RGB connector depends on whether the lighting system is the plain RGB type (4-pin, 12 VDC) or the more advanced Addressable RGB type (3-pin, 5 VDC). On most RGB controller boxes you get control of the RGB lights only, and fan motor control is done separately.
That case is described as including a non-RGB fan at the rear for exhaust, plus two (I believe) front RGB fans. It does not specify exactly what fans or their specs, and it does not say there is any RGB control system or buttons for fans or their lights on the case.
Your photo show three connectors. The smallest with 3 holes must be the fan MOTOR connector. That means it is of the older design, a 3-pin fan that requires its mobo fan header to be using the older Voltage Control Mode in order to control the speed. I presume the rear non-RGB fan has only ONE cable from it ending in a 3-hole connector like this, too. Let's deal with the fans first, and leave the lights to later. Since all three fans are of the 3-pin type, your best option to provide power and speed control of the fans us to use a simple SPLITTER and connect them all together to the only SYS_FAN header your mobo has. A SPLITTER is a simple device that only connects all its fans in parallel to the mobo header. It has one "arm" ending in a female (with holes) connector (either 3- or 4-pin) to plug into your SYS_FAN header. Then it has two or more output "arms" with pins that you plug your fans into. It has NO other types of arms. (FYI, a HUB is a different device that has a third "arm" type that must plug into a SATA or 4-pin Molex power output from the PSU to get power, but this device can only work with 4-pin fans you do not have.) Examples of Splitters for you
https://www.newegg.com/p/N82E168124..._re=Coboc_fan_splitter-_-12-423-163-_-Product
https://www.newegg.com/p/N82E168824..._re=Coboc_fan_splitter-_-82-422-016-_-Product
Both of those are 4-pin models, but they will work fine with 3-pin fans. The first is a 3-output "collection of arms" type, but is out of stock at that supplier. The second looks like a small circuit board and should be fastened down so it does not move and make accidental contact with the wrong thing. Any mobo fan header can deal with the speed signal fed back to it from ONE fan only. So these Splitters will send back to the SYS_FAN header the speed of only ONE of their fans and ignore the others. (This has NO impact on ability to control fan speeds.) The first one is missing Pin #3 in two of its three outputs to do this, so you must connect ONE of your fans to the only output with all 4 pins. The circuit board unit is marked as "CPU" on one of its output headers, and this is the only one that sends back its speed signal. You do NOT connect your CPU cooler to this. Just ensure that one of your CASE fans is plugged in there.
In BIOS Setup for your mobo (see p. 70), for the SYS_FAN header you will be using, ensure that the item "Chassis Fan Temp Source" is set to use the temp sensor on the motherboard, and not the one inside the CPU chip.
There still can be a problem with this. A 3-pin fan plugged into a 4-pin fan header that really is using only the new PWM Mode to control its fan's speed will always run full speed with no control. Many mobos allow you to specify in BIOS Setup for each fan header whether it uses that new PWM Mode, or the older Voltage Control Mode (aka DC Mode). Your mobo's manual does not say you have that option. So IF it is fixed on using PWM Mode, it cannot control the speed of any 3-pin fan. In that case, you need a different solution. Instead of a simple Splitter, you need a very specific model of Hub, the Phanteks PWM Hub. It is unusual because it actually "converts" from the PWM Mode to the older Voltage Control Mode, so it CAN control the speed of any fan (3-pin or 4-pin), BUT it MUST be fed from a mobo SYS_FAN header that really is using PWM Mode. Your mobo manual says that is how the SYS_FAN headers do operate, so this should work for you.
Now on to lights. Your photo shows two connectors with 4 wires and 4 pins (male) or 4 holes (female), suggesting those fans include plain RGB type lights. The case web page illustration also shows fans lit with only one colour at a time, and no rainbow effects; this also indicates plain RGB type lights, so we'll assume that. Thus you need a controller box of that type. Of the two you linked to, the second one - the cheaper LSB1 model you prefer- IS the correct type and the first one is NOT. (The first, model LSB02, is of the 3-pin type.)
I am going to speculate a bit here. You photo shows two 4-pin RGB connectors - one male, one female. I suspect that you CAN plug one into the other, and that these two both are on the same wires from the fan. I believe this is to allow you to connect two or more fans' RGB cables together in a "daisy chain" arrangement so that both of them can be connected to a single mobo plain RGB header. But you do not have such a header. Instead, you can get that Silverstone LSB01 RGB Control Box and plug the FEMALE connector from each of your front fans into box ports. The I suggest you wrap some tape around the exposed pins of each fan's male connector to prevent them from shorting out to Ground. And finally you can plug the two separate light strips that come with this Control Box into two of its other ports and use those lights, too.
That control box has a cable that must connect from it to a PSU 4-pin Molex power output connector to get power for the lights. On the Control Box (see its manual Step 2) the socket for this cable is shown at the END of the box, the socket on the right. Then it has cables for two options of how to do control. One way it co connect to a mobo 4-pin plain RGB header and use that to provide control signals, but you don't have that option. The other way uses a different built-in method. You must go to the mobo header near bottom front called System Panel Header (mobo manual p. 24) and find the two wires for the RESET pushbutton on the case front (the horizontal pair second from top). Disconnect those two wires and plug them instead into the LEFT socket on the box end. Now that case front RESET button no longer does the Reset function. Instead it has become the way to step through all the choices of lighting displays in your RGB fans at the front, and the light strips, too.
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