Definitely sounds like you are getting the runaround on the tile. Having done quite a large number of damaged/cracked tile replacements on jobs I was not originally involved in, I can tell you that it is not unusual (especially with "clay" and "quarry" versus "ceramic" or "porcelain" tiles, for there to be size differences up to a half inch or so for large format tiles.
1) cut tile to fit, rounding the cut edges and putting on colored tile instant glaze or permaglaze (or other names) which is actually an epoxy to a close match in glazing color. You can run the grout a tad high in that joint to cover up most of the cut/rounded surface to minimize the exposure of the variation in color.
2) search through several boxes of matching tile for tiles that fit.
3) usually only done for high-end jobs, is ordering custom size tiles from the manufacturer - most will produce custom prices for in-production lines, or take custom cut tiles you send them (for out of production they did not keep a sample of) and work up a custom glaze to approximately match, then reglaze and refire the tile. This is not cheap, of course, especially when you include shipping cost for heavy, highly padded tiles, but can produce an almost perfect match.
I would be sending a nastygram to headquarters about their poor punchlist performance, because it certainly does not sound up to snuff. I have to have some sympathy for the builders in this situation too, because they are dealing with a world of contractor managers and workers where it used to be maybe 10-15% were incompetent, did not care, were drunks, etc. Now it seems well over 50% of workers could not care less, have no work ethic, or are on drugs or drunk. I have worked remote site, high-risk industry, and government jobs with mandatory drug and alcohol testing where over half the prospective new hires or current workers failed the tests - and that was just the drug and alcohol fail percentage, not including the ones who could not care less or had zero work ethic ones who are the result of the spectacular education and parenting failure of the permissive society and teaching to high "self esteem" rather than performance. And that does not include the high school graduates who cannot make change or do 4th grade math, but were let through the system regardless of failing grades. Glad I am retiring from the business - it is just too hard to get a quality crew to produce a quality product these days.