You've probably got worn wishbone bushes, the rears most likely. This new (old) tyre clearly has less mechanical grip than your last set.
As you accelerate, the wheel moves to a toe-out position, then when it loses grip, it snaps back to toe-in - this can be made worse by a sloppy lower engine mount allowing that to shift around as part of the process. It only really happens at certain low speed, so you may not have noticed it before if the old boots allowed you to launch past it. Heavier wheels make it worse too.
Old fix was a WALK, although I believe the Superpro version is cheaper and possibly better.
