Just looking at this video there does seem to be several things going on here. First off I know its not a mustang...
It looks like the first effect is an increase in speed from the rocket motors firing, followed by a reduction in parasitic drag as the rocket leaves the airframe. This asymmetrical drag although momentary may force a "recoil-esque" feel in the controls. That all being said (not an expert here) I do think the effects of firing the rockets on the Mustang may be a bit overstated.