How to connect a four route MOSFET to multiple power sources?
Looking at the device schematic on your linked page, I see that the power + terminal is directly connected to each output + terminal, as well as the internal circuitry. Therefore, you are free to connect the plus side of each load (LED strip) to either the output + terminal or the plus side of the 12V power source.

Just make sure that you do connect the power terminals of your MOSFET board, even if you don't use the plus output terminals.

Edit: the OP clarified that he wants to use a separate 12V source for each LED strip. This is fine. You can do the following:


Connect all negative leads (from power supplies) together and to the MOSFET power input connector.
Connect each positive lead to one LED strip. Chose one of the power supplies and also connect its positive lead to the MOSFET board power connector.
Each LED strip negative lead goes to the negative side of the corresponding board output.
Do not connect all of the positive leads together!


Each power supply will power one LED strip. One of the supplies will also power the board (very little power draw).