Wrong, unfortunately. That AIO system specifically states the lighting in the pump and fans is the simpler plain RGB system (4-pin, 12 VDC power) and NOT the ARGB system (3-pin 5 VDC). It comes with a small hand-held RGB controller you do NOT need because you can do it all with your mobo's 4-pin RGB headers - there are two, see manual p. 1-16. You'll need to use only one of those because the fans have lighting cables with two connectors on them to create a "daisy-chain" connection system. You start by plugging one fan's lighting cable FEMALE (with 4 holes) connector into one mobo RGB header. NOTE that the header has the pin at one end marked as the 12 VDC power line, and each connector has a mark by the hole at one end for this line. You MUST match those two at EVERY connection point. Then you plug the female connector from the second fan into the male (with pins) output connector from the first fan. Repeat for third fan. Finally, the female lighting cable connector from the PUMP unit goes to the male of that third fan. So all units' lights are fed from one mobo header. Once this is all working you will install and use the ASUS utility Aura Sync to configure our lights as you like.
You were wrong to label your AIO system as 3-pin lights. But MAYBE you were confused because ONE of the cables from your PUMP unit has 3 holes. This is the PUMP motor power and speed connection. It should go to your mobo CPU_FAN header. The Splitter supplied with that system to power the three rad fans should go to the mobo CPU_OPT header. In BIOS Setup, go to each of those headers and look for a choice of MODE - usually Votage (or DC), PWM, or AUTO. Select PWM for BOTH headers to ensure the pump will operate at full speed as intended, and the 4-pin rad fans' speeds will be controlled automatically.