it's not a rule that it SHOULD always run when A/C is on, but it should do it's job - which is maintaining the temperature.
my observation is, in peak hot summer temperatures, whenever i keep the blower fan speed to 1 position, the fan keeps tripping on / off , but as i switch the blower fan speed to 2 position (or onwards) the fan did not stop even once in 15 minutes of testing ...
BTW, my car has only one fan for raidator and condensor.