As I understand from my reading, mask pressures get increasingly tighter with depth - yes? Perhaps at 20 feet my mask would have been just right and not leaked and the instructor was bang on. But we were doing pool drills at about 3 feet under, which probably didn't have enough pressure to seal the mask in the way he was, in his overly hurried state, thinking it would. This could have been solved if he took more time to seriously examine my concern and wasn't in such a rush.
Your mask is one of those air spaces you equalize. So yes, if you ALLOW it to squeeze onto your face it will and it will also be painful. A simply puff of air from your nose will equalize the space and you will be good to go. The mask itself would appear to be a moot point and your main concern was the lack of assistance/instruction from the instructor.