I thought the CPU pump fan header would control everything?
The pump header does not control RGB. Nor should it control fans. Your motherboard should have separate fan and RGB headers, if you want to use fans with their own dedicated RGB inputs.
Although I've never used an AIO, it is my understanding the pump should be connected to one header, sometimes marked CPU_Pump and run at a constant +12V.
The radiator fans (all of them) should be plugged into a different mobo header, often marked CPU_Fan.
So I'd expect to use three mobo headers, CPU_Pump, CPU_Fan and RGB. You might have to use a header marked CPU_Aux if the CPU_Pump header does not exist.
I doubt if your motherboard is capable of running the pump motor plus 3 radiator fans on the same header. There's often a current limit of 1A per header and you might exceed this rating with 4 items connected (pump + 3 fans).
Your motherboard manual should explain the correct pump, radiator and RGB connections. Your link to the German Arctic web site doesn't work in my browser.
As for separate RGB lighting, I've never used it. Take care not to connect your RGB plugs into an incompatible mobo header or separate RGB control unit. You can damage RGB with the wrong voltages. If in doubt, leave the RGB disconnected and find someone local to help you. Better than killing your mobo or fans.