12V pump will require 12V PSU. 20LPM is a pretty reasonable flow rate for a small pump so your pump PSU will need to have enough power to drive the pump - check the max current draw on startup (which will be higher than the running power draw) and size the PSU accordingly.
Check the contact handling voltage/current for your relays.
"5V" relays (as described) are more likely to be "5V trigger" (i.e. the coil requires a 5V signal to activate) rather than 5V contact (which would be a very small relay contact voltage). Most relays will have contacts rated with both a maximum voltage (V) and maximum power handling (VA). The maximum power handling for your contacts needs to be higher than the maximum power draw for your pump (as previously noted - this usually occurs on startup). I would factor in at least twice the "running power" requirement if you don't have startup power specs.
Also note that the contact PSU must be fully isolated from the RPi PSU. This is how most of the relay HATS are designed - as it protects the RPi from overvoltage. Also a small flyback diode (watch polarity on DC) will help to protect from transients (voltage spikes) that can be created when the contacts open/close. This may already (read should) be supplied on the relay HAT if properly designed.
Looking at the spec sheet (http://www.circuitbasics.com/wp-content/uploads/2015/11/SRD-05VDC-SL-C-Datasheet.pdf) for the relay blocks supplied in the image (SONGLE SRD-05VDC-SL-C) the relay is 5VDC trigger but the contacts are capable of handling :
Resistive loads : 7A/28VDC 10A/120VAC
Capacitative Loads : 3A/28VDC 3A/120VAC
Max Power : 800VAC/240W
So, if your motor falls within these specs (i.e. less than 240W power draw on startup) you should be able to use the circuit in the image. Just swap the 5V pump PSU for a 12V PSU and the 5V pump for a 12V pump.