"Moving seat" has two different things it can be.
One is the normal "give" of the seat. The seat is a semi-rigid object that you can press back into, has padding, and so on. This is normal and to be expected. If it is a springy and squishy feel, it's normal.
Then there is shifting. Shifting is differentiated by a sharp motion that happens and stops. Shifting has a distinct hard end to it and often a "clunk" feel or even sound. It is jarring and can actually be painful. Shifting is NOT normal. Shifting is bad. My car just got back from the SC to correct shifting that was caused by improperly torqued bolts on the seat. Mobile usually cannot fix shifting because the bolts used have bolt lock pre-applied, and the shifting kills the bolt lock, so new bolts are needed. Just tightening down the bolts ends up getting loose again in short order.