Since I have not seen the play(s) in question, I will not comment on the legality of the QB's movements. However, I have included the rule reference that would pertain to this type of movement.
I hope this answers your question.
Rule 7 Section 1 Article 2
Shift and False Start
ARTICLE 2. a. Shift. After a huddle (Rule 2-14-1) or shift (Rule 2-22-1)
and before the snap, all Team A players must come to an absolute stop and
remain stationary in their positions for at least one full second before the ball
is snapped, without movement of the feet, body, head or arms (A.R. 7-1-2-I).
b. False Start. Each of the following is a false start by Team A if it occurs prior
to the snap after the ball is ready for play and all players are in scrimmage
formation:1. Any movement by one or more players that simulates the start of a play.
2. The snapper moving to another position.
3. A restricted lineman (Rule 2-27-4) moving his hand(s) or making any
quick movement. [Exception: It is not a false start if a Team A lineman
immediately reacts when threatened by a Team B player in the neutral
zone (Rule 7-1-5-a-2) (A.R. 7-1-3-V)].
4. An offensive player making any quick, jerky movement before the snap,
including but not limited to:
(a) A lineman moving his foot, shoulder, arm, body or head in a quick,
jerky motion in any direction.
(b) The snapper shifting or moving the ball, moving his thumb or
fingers, flexing his elbows, jerking his head, or dipping his shoulders
or buttocks.
(c) The quarterback making any quick, jerky movement that simulates
the beginning of a play.
