Oh dear...
Firstly i don't like picking holes in anyones work, anyone can be an expert if something goes wrong, but..
As Robson says, dot and dab is never acceptable ever ever ever etc. No builder should except a tilers work that has any hint of dot and dab, and for him to be unable to gaurentee it won't happen is unforgivable, he should be kicked off site, he's wasting your time and money and the builder' reputation. Maybe the majority of 'tilers' do that because there are lots of people claiming to be tilers that don't have a clue, or just don't care, it gives us guys who care a bad name and takes work away from us.
The tiler hasn't explained to you the difference between 'level' and 'flat'. If you hold a CD case in your hand it is 'flat', but if it is tilted then it isn't 'level'. Many floors can't be leveled as you could get huge height differences between door openings etc, but should always be flat. I see he got the floor flat but was he trying to 'level' it too, explaining why he tried to raise the tiles by dot and dabbing, if the floor wasn't 'flat' enough he should have sorted it before tiling.
Why didn't the leveling compound (not leveling cement) stick to the boards? My guess is it wasn't quality gear and certainly wasn't primed.
The tiler should be preparing his own floor, not the builder. The tiler should come and say if he is a happy with the prepared substrate, both the concrete and the wood, if he isn't happy he should voice his concerns and explain what needs to be done, and not proceed until it is done, this floor will be his resoncibilty.
Then he would prime as required lay the under floor heating and level over the top. This is his job, not the builders mate, why would he get it flat and why would he care if he didn't.
Then the next day proceed with tiling if he deems the floor 'flat' enough to take large format tiles, if not add another layer of leveling (or self smoothing compound as it is often called now), to make it flat. When he lays his tiles he will comb the adhesive onto the floor, back skim the tiles and not, ever ever ever dot and dab the tiles to the floor, if a tile is high or low he adds or removes the adhesive needed all over the tile so that the adhesive is solid bedded into it. Any voids are a weak spot.
You did cause the dot and dab to fail, because you walked on it and it was not laid well enough in the first place!!!