Turning an AC unit off for a couple of hours has absolutely no negative consequences to the unit itself. The stuff about compressors was bullshit that the manager hoped would not be challenged.
We don't really know what the concern was, because our sole narrator wasn't paying attention when it was voiced. However, if the "solution" was to keep one AC unit off while running the other one I could see there being a concern overtaxing the single running unit.
So the manager just wanted to leave the AC on all night for no reason? That makes no sense.