Yeah normally i wouldnt get that technical either but OSB or actual plywood is huge in this case. They got the right plywood at least. How old is your floor?
I do hope im wrong that this floor is not a complete failure but grout popping out like that is a huge red flag. Next time they come out to replace a tile watch them do it and ill bet you $100.00 the tile will come off clean with little force and either have no thin set adhesion on the tile or no thinset adhesion on the plywood, sorry if thats confusing but you'll know what i mean when they take the tile out.