If they are tiling in a customers property, they should know what they are doing and know what preparations are required. I don't see why you should be out of pocket for poor workmanship.
Obviously we don't know the correct procedure or time scales, but there will be tell-tale signs to show if they kcufed it up.
Example, if there are no expansion joints, thats the first thing, because if the job is over 36 square metres, they have not complied with British Standards (BS5385).
If the tiles are loose, lift a few up. If the adhesive has stuck to the tile but not the floor, they have probably used the incorrect adhesive or have not primed the floor correctly.
Lifting the tiles may also show any cracks in the asphalt, which could mean that either the underfloor heating was incorrectly commissioned, or the heating has caused excessive expansion beyond the capabilities of the adhesive (this is one of the things that the Ditra would have combated), which also means asphalt was totally the wrong choice of substrate to tile onto. It may also be a sign that it was tiled too soon after the surface had been laid.
If the grout joints are less than 3mm wide (the minimum required by British Standards), there's you're 4th issue to raise with them.
Quite simply you have enough to raise a complaint against them. The very least they should do is come to your property to examine it. If the tiles have come unstuck, there is a reason for it. and if you had nothing to do with the installation of the tiles, the liability will lay with the house builder and installer. Hope this helps, but if you need any further info let me know. Better still if you can post some images of the whole area and close-ups of the loose tiles (and whats beneath them after the tiles have been lifted) I'll be able to advise further.