In what crazy world would it move in a bit? That’s BS.
There are 2 types of square taper fitment, it sounds like your fitment is okay but the cranks are made for different bottom bracket widths.
I don’t know if there is a database of crankset and BB combinations anywhere, but if you can live with it, crack on.
It would drive me nuts and you might find it’s probably easier to get a new BB and crankset combination rather than luck into the correct combination.