Mill dyeing is done under circumstances that cannot be duplicated on a floor. If you have a nylon carpet, take them a couple of toothbrushes and have them dye the bristles. Take them home, run some tests on only one. Does it fade or wash out in a sink, in a dishwasher? Are you going to have your carpet cleaned? Does it fade in sunlight? Does it change color in lemon juice or vinegar (acid), or in sodium carbonate or borax solution (alkali)?
This is not to say that they are not competent. See what they do, read the contract closely. Know what you will be promised and know what you can recover if the promise does not obtain.