It is possible, with the use of the appropriate capacitors, etc., to "create" a third phase. It's won't be true three phase, but it will get things spinning the right way.
I'm not about to try to explain the 'how' or the 'why' .... but, since you mentioned that the tap hook-ups were unusual, it is possible that something like that was done.
The other thing you said that caught my attention was "auto shop." I have seen more screwed-up compressor arrangements in auto shops that in all other locations combined. I would almost say "if you saw it in an auto shop, there is no way what you saw was correct."
I suspect that, if you checked, that the motor is performing very poorly. That is, running hot, gobbling power, and not performing anywhere near its' capacity.