And there is indeed a momentary sideways motion of the rocket. At T+1.7 sec (1.4 sec after first motion) the Apollo 11 Saturn V executed a 1.25 deg yaw maneuver away from the tower to give it a little extra margin against wind pushing it into the tower. This maneuver ended at T+9.7 sec, about the time of tower clear. At T+13.2 sec it began the roll and pitch maneuver.
BTW, the white stuff is actually coming from the outside of the LOX tank in the upper half of the first stage (the RP-1 fuel tank at the base of the rocket is at ambient temperature.) The entire tank is covered with ice, which is why it's white. Much of it fell off at liftoff, which it's starting to do here.