There are some tile that try to mimic say ungauged slate where the tile will vary dramatically in thickness that are next to impossible to get flat and are not made to be flat anyway.However,after saying that the majority and i mean about 99% of the tile is meant to be installed flat with no lippage.
If there was a problem with the subfloor in needed to be addressed BEFORE the job started not after it was finished.If he did the job then he owns it and he needs to get back there and fix it.
Did you already pay this guy?Hope not but if you are having difficulty getting this guy back then it sounds like you did.
Call the refferal co.too and lean on them a little bit,maybe they will have a little clout with him and they will be able to help you get this fixed