Replacing ceramic tiles on floorboard?

Hmm..trying to understand your Q's- uming that the builder is too lazy to remove the existing floor board on top of the cement slab and he's trying to lay directly onto the floor board instead. The answer is a 'No-No!'. Ceramic tiles requires cement mortar to adhere to cement slab - hence there's no adhesion at all. Wet mortar won't bond to the floor board & furthermore the wetness will rot the wood! He may argue that he's using special adhesive but again such adhesive has limitations- subject to the floor substrate being free of dirt, grease, undulation, wrap, etc. -read the label of the adhesive. Basically, it's not advisable to do so as in the long run the floorboard may crack, wrap, move resulting in the tiles ontop being pop-out or debond. Furthermore your have cut the bottom of the doorleafs, higher levels compare to other floor areas, etc. Ask him to remove it..and you will safe long term hals and risk the repair or replace of tiles later on. Be safe then being sorry. Ta ta & good luck.