Can you tile on finished plaster wall in a shower?
I have repaired tile jobs that were over 20 years old that the tile was applied directly to regular sheetrock and plaster walls. This was back in the 80's. It used to be very common to put tile up on whatever the wall was and seal the the tile. More recently I have seen some contractors still put tile up with out a backer board to save $ for the owner especially for flipping a property. Is it the best way? NO. Will it work? Yes. Maybe several decades if well sealed. All the frame work around showers and tubs I have installed has been wood, again if sealed it will last for quite a while if there is a slight angle to prevent water from pooling on the ledge or box. You should have received a quote prior to the start of work that you agreed to (the law in my state) it should define the scope of work and materials. For what it is worth if cement backer is not included the contractor may be matching the existing tile job.