Manufacturers of those floor heat systems say you can apply one of two methods to prepare the floor for tile after the heat system is installed.
One thing is to spread thinset over the system then install the tile.
The other is to pour Self Levelling Compound (SLC) over the system.
Self Levelling Compound can get expensive so the cheaper method is to spread the thinset. The makers of floor heat offer up the thinset method simply so that the cost of installation of their heat product doesn't look so expensive as to discourage sales of their product.
The problem is the "spread the thinset" method isn't at all practical and in some cases isn't at all do-able - you see the results when put into the hands of inexperience.
The only practical way to cover those heat systems is with Self Levelling Compound. SLC's also offer the consistent "thermal-mass" that is needed for your system to operate properly.
This installer guy had no idea what he was doing and should have told you that up front. He should of also offered the SLC option but he obviously wasn't aware of the pitfalls of the thinset method. This tells me you were his first floor heat client.