Agreed, that is correct. The background issue is that this is a very powerful pump and it uses 1.8 A max current. A mobo fan header normally is limited to 1.0 A max. So this pump has TWO separate wires sets. One pair goes to a PSU Molex output to get that power. The other, which ends in a 4-hole female fan connector, carries the lines to feed the pump's speed signal to the CPU_FAN header, and to get from that header the PWM speed control signal. This latter REALLY should be plugged into the CPU_FAN header. One of its functions is to monitor the speed of its "fan" (in this case, the pump) for FAILURE - that is no speed or a speed lower than some minimum setting. Failure triggers rapid warnings and, on some mobos, quick shut-down of the system without even waiting for a high temperature reading from the CPU chip's internal sensor. In a liquid-cooled system, failure of the PUMP is more critical that failure of the fans on the rad. So it is important that this connector go to the CPU_FAN header. On some mobos there is a second header for an AIO PUMP, and this can be used because it also pays careful attention to the speed of its pump. BUT many of these headers by default are set to run the pump only at full speed (you MAY be able to change that in BIOS Setup), which this Phobya unit does not require.
Many liquid-cooled systems are designed to run the pump at full speed all the time. This controls the internal CPU temperature entirely by changing the FAN speeds on the rad. To configure a temperature control system with TWO devices - the pump speed and the fan speed - being changed independently is extremely difficult and can lead to temperature cycling and instability. On web pages I found no such instructions for using the Phobya pump (it is not part of a complete AIO system), but maybe there are instructions on this point in the material included with it. The fact is, though, its design makes it possible to control the pump speed from the CPU_FAN header. Leaving that header in the default "Standard" or "Normal" Profile will change its speed constantly, and that may NOT be the best strategy. But you have two other options normally for that header. You can set it to constant full speed. Or you can set it to a constant lesser speed if you feel your CPU cooling does not need all that fluid flow. Either of these choices would remove the effect of pump speed changes and make it much simpler to use automatic cooling control of the CPU by another mobo header that controls the speeds of the rad fans. For that purpose, it would be important to set that header's TEMPERATURE sensor (IF you have the choice) to use the one inside the CPU chip, and not the one on the mobo.