Most Nissan ecu will cut the A/C compressor when you rev the engine and also when is overheat, this is to protect the a/c compressor when engine is revving high, and give more cooling capacity to the radiator / engine when overheat detected.
It will cut in climate control but not so frequent. Climate control a/c system use hot air "from radiator water" mix with cold air "from A/C cooling coil" to control / reach the temperate driver set. Is difference from the normal A/C in the car, where you feel a sudden cold then not cold then cold again.
I heard there are new type of climate control system, but did not really go into detail which car have it or how it work.