A/c fan operation.

[mrpj]

My 2014 French Yaris was main dealer serviced a month ago. It has dual climate control which I set to auto, a/c on and 20degC.
Prior to the service (could be coincidence) and when switching off the engine I could hear the cooling fan coming to a stop. The fan would not be running because the water temp. was high but presumably because the a/c was on.
Since the service I no longer hear the cooling fan running down. I have checked under the bonnet with engine running and the a/c on and the fan starts and stops in conjunction with the a/c compressor loading and unloading.
So after the above ramble, does anyone know which is correct before I contact the dealership and possibly make a fool of myself!?
Should the cooling fan run continuously when the a/c is on or should it stop and start in time with the compressor unloading and loading?
Stopping and starting would surely be no good for the fan motor and the fan relay.