If they just evacuated it then it should not have run when they started it.
The same is true on my truck, incidentally; no charge, no run at all. The truck (a GM) has a sensor on the low side so when filling it the compressor will cycle until the low side pressure, while running, is high enough for the clutch to remain engaged. It also has a high-side sensor and clutches the compressor on and off during normal operation (depending on the temperature of the cabin and where the dial is set, of course) -- as does my Mazda, although I've never had a reason to screw with that car or take it to someone for A/C work as it's reasonably new and everything works. The ALH only has a high-side sensor and the compressor is variable-displacement so once it comes on it should stay on since once it comes on the pressure will rise, of course, on the high side. The only thing that should kick off an ALH compressor with the button in if there's refrigerant in the system is if ambient temperature is too low, during full-throttle pulls or if the coolant temperature gets too high (in those cases the ECU will shut the clutch down.)
It makes no sense that they evacuated the system, put nothing in it, then said "it doesn't run so it's broken" in short -- I can't speak to all auto A/C systems but certainly neither my truck or ALH will pull in the compressor with no refrigerant in them.