Has, those pics certainly concern me! Especially the 2nd one! Your tiler back fills, not 100% sure of what he means but going by pic 1 I'm guessing he is going back and filling the voids left when tiling.... 2 issues with this, he can maybe back fill, but you can't front fill or middle fill as you have no access thus no pro tiler would do this! ...hope I'm understanding situation correctly here
You need to be getting as close to 100% coverage on a floor as you can, especially with stone such as marble! .... I'm not seeing this here!