Mastermapmaker
Hey, It's not needed.
The physics are computed relative to the zSolver, which is why moving it in lockstep with the character over one frame during run up works.
Under "normal" circumstances, if you want the character to look as if it's moving "through the world" don't move the solver after runup.
If it's a shot where the character has to go through large accelerations and/or decelerations though space over a short time, you can move the solver in lock step with the character as a "trick" to negate the inertial effects that accelerating/decelerating quickly might have on things like secondary motion.
Hope that helps!
Andy