Unfortunately I could not find any instructions for installation of the Asetek 510LC system. So all I can do is recommend on general principles.
Most AIO systems are designed so that the PUMP operates at full speed all the time and requires NO speed control. ALL of the control of CPU cooling is done by altering the speed of the RAD FAN, so that fan does need mobo-based automatic speed control that is guided by the temperature sensor inside the CPU chip. That sensor is always used by the CPU_FAN header, and usually also by any auxiliary CPU headers such as CPU_OPT, etc. SOME mobos also allow you to configure a CHA_FAN or SYS_FAN header to use the CPU chip's temp sensor instead of the motherboard sensor.
A fan header has TWO functions. The first is to alter the fan speed in response to the actual temperature measured on the "hot spot" (the CPU chip or the motherboard) that the fan is cooling. But also important is the secondary function of monitoring the fan for FAILURE, interpreted as a fan speed reading that is zero or less than some specified minimum. Now, when it comes to AIO systems, you have TWO components to monitor for failure - the pump and the rad fan. On many mobos the CPU_FAN header (and often a few others such as CPU_OPT and PUMP headers), the failure monitoring system takes quick action if failure is detected. It certainly will send out a warning message on-screen. But it may also initiate a complete system shut-down without even waiting for the CPU's internal temp sensor to report excessive high temps. Some even refuse to let you start up if there is NOT fan speed signal getting to the CPU_FAN header. This is all to ensure that the CPU never overheats so badly and quickly that it is damaged.
Given those points, my preference IF you can is always to connect the PUMP to the CPU_FAN header because failure of that item WILL cause failed CPU cooling and rapid temperature rise. Failure of the rad fan, on the other hand, will cause a slower temp rise inside the CPU because some of the heat still is being carried away to the rad. However, that also depends on whether you do have a good way to control the rad fan speed.
And here's another fine technical detail. Any 3-pin fan connected to a mobo fan header that actually is using the new PWM Mode of control for 4-pin fans will always run full speed. So, many AIO system makers supply their PUMP wired just like a 3-pin fan and expect you to ensure that the CPU_FAN header you plug it into (or other header) IS configured to use PWM Mode. That way the pump does actually run full speed all the time, as intended. PLUS, if you plug the PUMP into the CPU_FAN header, its speed is monitored properly for failure. m(Actually, I note on the Asetek web page for this cooler that it claims the pump unit does its own speed adjustments internally (does NOT use the mobo header speed controls) based on its own sensor of the temperature of the circulating liquid. That is an unusual design!) But then you still need some fan header that uses the internal CPU chip temp sensor to guide it so you can plug the rad FAN in there and control its speed (and hence the CPU cooling) that way. If you have a CPU_OPT header, that is ideal for that. Alternatively, if you have a CHA_FAN or SYS_FAN header that allows you to use the CPU's internal temp sensor to guide it, that also can do well for the rad fan.
OP, you say the system you have has 3-pin connectors on the wires from BOTH the pump and the rad fan. That makes it a bit tricky because the 3-pin fan MUST have its control done using the older Voltage Control Mode (aka DC Mode), and that must be done by a header that can use the CPU temp sensor. BUT you do not want the PUMP to be fed from a header that uses that Mode, because its voltage should NOT be reduced at low CPU temps. So you need separate headers for those two items, and it is desirable that the PUMP at least (and preferably also the rad fan) be monitored closely for FAILURE just as a CPU_FAN header would do. To be sure we give you the best advice, post back here the maker and exact model number of your mobo so we can examine the details of how its fan headers operate.