Wet cutters do a better job, and sometimes, you'll need to do a few test cuts to find the best method that works for a particular tile. I've just worked on some 9mm porcelain tiles, and they cut like a dream on a cheap 600mm manual cutter, but I doubt it'll work so well on the polished porcelain that I've got to do next.
Just look them straight in the eye, and ask them if they consider it an acceptable job, and when they say yes, just tell that you don't, and they'll need to redo it if the want paying, else you reserve the right to get someone else to redo the work, and they'll have to pay for the replacement tiles as well.
Try asking them to show you other jobs they've done where the tiles have been chipped.