No, once the footrest is extended it will not be affected by the tilt of the back of the chair. The footrest on all of these chairs is attached to the underside of the seat, and since the seat isn’t affected by the back tilt of the chair, the footrest is not either.
Basically, the footrest will only move when the seat does, which will only be up and down thanks to the gas lift adjustable feature on all of the chairs that allow you to adjust the height.