It is not so much that the tub moves, but that I can feel the bottom of the tub flex with my feet as I move. I have never noticed this in any tubs I have had previously.
If it was moving, the builder would be replacing.
When I set my tubs I make sure the carpenters use 3/4 CDX plywood under the tub.
I personally nail the tub to the stringer I have installed along the length of the tub.
I have a firm footing installed with TWO upright braces and a 2 4 under the tub lip for added support.
THEN I have the tile guy set motor under the tub and have at least a 2″ cement depth (not so deep on Cast Iron).
Fixtures are not meant to flex