Well good for her following the instructions on the bottle. And shame on you, getting your dear old Mum to clean your kitchen floor
Matt doesn't necessarily mean unglazed but it really really depends on what it says on the box of tiles (or the info leaflet with them). I'm no tile expert but I have seen some that look as if the pattern has been printed on with an inkjet, it worries me that the pattern would scuff off in a heartbeat.
I don't really like super shiny tiles (bit like having a black car, one speck of dust or one slightly off level screams at you) but modern cleaning materials can contain quite aggressive chemicals. It does say on the bottle 'test in an inconspicuous area first'. I'm very lazy, keep looking at miracle oven cleaners but when you get to the small print they all tell you not to use on enamel. Which is what cheap ovens are made of. So back to the Flash and the elbow grease
Don't think it has stained the tile, more like washed some of the pattern off. You'd get a similar effect if you use Jif (if it still exists) on an enamel bath- the particles of whatever that were in it will take the top off the enamel in no time and leave you with a nasty rough bath that can't be cleaned.
Got to say, valley floors' website is a bit useless. No info on how thick the tiles are, what adhesive or grout (waterproof or not) is required, no clue as to where they're made. Mind, Topps' website isn't a lot better but at least they give you a price. They're both a bit like estate agents' descriptions- you have to look for the words that aren't there!
I'm fairly certain it is an aesthetics thing only- the floor will still function as a floor. Please don't paint the tiles (there's a really annoying advert playing in Toolstation at the moment advertising some miracle paint- picture shows a closeup of someone putting this paint on a tiled wall and it looks absolutely dreadful). If you can find anything from the tile packaging or from Valley Floors that says your tiles are glazed then they've got a case to answer, if not then put it down to experience and move on. As for remedies- forget it.
PS Have you noticed how many shopping centres have highly polished glazed walkways? Yes they're slippery WHEN WET so don't chuck water around the place and you'll be fine.