My assumption is that the 12 inch movement is just to help cement a sense of scale (helping resolve the question" how far would a mausritter move in however long a round should be?") . Naturally if you wanted to lock things to a grid I imagine that would be OK, but it seems like you'd have a bit of work filling out the details.
I'd more look at it as a way to help imagine whether they could run to the other side of the book they had vaulted on before the cat reached them, that kind of thing.