The fans don't kick in with the compressor, if you look at the TSRM the fans are controlled by a HI pressure switch. You also might want to check if you have enough refrigerant and NOT bypass your HI/LOW switch. Running your system when you are low on freon probably isn't the best idea.
There is also a water temp switch that will turn OFF the A/C if the temp is too high. Mine was failed and wouldn't allow the system to turn on.