I dont know how this will affect whether the fans start and stop due to a thermostat. But it seems logical that the aircon condenser fan would run constantly while the aircon compressor is engaged. If the cabin temperature indicates the aircon doesnt need to run constantly I would have thought it more fuel efficient to disengage the compressor (and the fan at the same time) . If it runs constantly maybe the aircon is not cooling the cabin very efficiently. Have you checked the cabin air filter?
When the compressor engages it puts more load on the engine ,which may produce more heat. The ECU may engage the engine cooling fan to overcome this extra heat, actual or anticipated. If the aircon fan and compressor are not disengaging ,for whatever reason, ,maybe the engine fan wont do so either.
A further thought, but just a theory. . If you use the aircon in the winter the system may be programmed to assume you are using it to dehumidify the cabin rather than cool it. Maybe a cold outside air temperature overrides the cabin temperature and allows it to run for longer, as it wouldnt be easy to detect how long you need dehumidifying.