Sorry, just got back from out of town.
Freezing with liquid nitrogen is an "art", just like automotive body work!
If you don't freeze long enough, you don't kill the tissue and it survives and nothing (or not enough) comes off.
If you freeze too long, then you can make too deep a "gouge", and then that leaves an obvious "divot" and doesn't look good and people aren't happy.
So your guy just erred on the short side and didn't freeze long enough to get it.
You should call and let him know that it didn't "take" and what does he want to do. The answer should be, "Come on in again and we'll do it again, and there will be no charge."