If you go to the Warm Tiles web site you can see an interactive tutorial of installing the system over a plywood subfloor. Double 5/8" subfloor, install the mounting strips and install the heat cable, embed the cable with thinset, then thinset and tile. Sounds like your installer is unfamiliar with the product/install and is getting jittery about it. You or the WarmTile vendor probably need to go over the install procedure with him.

I just installed heating cable from Warm tiles, it was reasonably easy thing to do. I have not used mounting pieces of metal that came with it as they seems did not want to align well for me. I placed my initial layout fixing cable to the floor with aluminum tape and then went with hot glue gun and glued cable to the plywood floor in chosen spots. Tape got removed prior to thinset application. The splice, end piece and sensor that came from thermostat box are of larger size and plywood floor needs to be chiseled down in areas where they are to go. I believe it is pretty common for any type of heating mats installation not only the cable.
Make sure you have some kind of good underlayment to go along with plywood. I think most common will be cement board and then you apply your cable over it or newer uncoupling membrane Ditra, which goes on top of cable. Hopefully other pros will chime in but my understanding that is it not a good idea to lay cable over the plywood only and then tile over it, your tile won't last long that way- too much stress.