His knees go forward because in the olympic lifts u use something called a "double knee bend". As u probably know, when ur ass goes too far back u end up removing the quads from the movement, the "jumps" in weightlifting or in any other sport is initiated by the quads, not the hips. When he pulls from the floor, the bar has to pass the knees meaning the knees will be pushed back and ur ass will be back resutling in little quad involvement, so he pushes his knees forward after the bar passes his knees so that he get's some bend in the knees shifting some of the force back to the quads.מה לעאזעל הולך לך עם הברכיים.
It's basically a trick to get ur quads back into the movement.
The hips shooting backwards in a squat usually is a sign of weak quads, the movement is supposed to be straight, but I suppose they want to engrave the "double knee bend" so they add it to the squats as well.. (biomechanically it doesn't rlly make any sense for lifting more weight.)
EDIT: this is also one of the reasons WLs insist on doing HB squats because it resembles the movements used in WL more than a LB squat, while Rippetoe say they should be doing LB instead due to greater muscle recruitment (which is true, but besides the point). Probably the only thing I completely disagree with Rippetoe on...