I agree with the expert above, the caulking tubes are for just that, caulking. There are some high performance pre-mixed urethane grouts that would be a much better choice. One brand is Quartz-Lock II. It remains flexible, is stain proof and sticks better than cheaper Acrylic pre-mixed grouts. Not an advertisement, just an endorsement and advice from someone who works with flooring every day. epoxy grout has good adhesion, but not as flexible, and harder to use.
I wouldn't be afraid to have a dealer arrange to have your tile replaced. a local tile setter can probably do a better job than a factory worker doing curtains one day, and tile the next.