I've been meaning to respond to this post since Wednesday, but it has been a busy week.
Coach Boeheim generally doesn't care which side of the floor the guards and forwards occupy in the zone. Their responsibilities are the same on either side since we play ball-position defense. What's important is that they are in the proper alignment and rotate accordingly as best as possible from start to finish on a given possession.
The weak-side forward is always the key player in our zone. It is vital that he rotate properly when the ball enters the high post, either by pass or dribble, or when we trap in the corners/short corners. He must closeout on the wing player on his side if the ball is swung quickly side-top-side, and then he needs to "bump" rapidly to the corner to closeout on any shooters when the guard recovers. (Roberson was yanked a minute into the BC game for not properly doing this two possessions in a row. After re-watching it, I'm not sure that Joseph was really late; Roberson didn't respond as if he was aware of the shooter in his corner. He has to closeout on the shooter with more urgency.) The weak-side forward must also be aware of the back screen that can set up lob passes and skip passes for three-pointers. Finally, he has a tough rebounding responsibility when a shot is taken; he often must get position between two potential offensive rebounders and fight hard to get a piece of the ball.
That said, Coach B has said many times that you can't play zone without knowing how to adjust it to the opponent. For example, if he feels that Silent G is the most skilled forward in terms of closing out on shooters, he may instruct G to always play the side of the floor from which the other team's best three-point shooter tends to shoot the highest percentage.
In that situation, he may also instruct G to shade that shooter every time that player is on his side of the court, so G would not rotate or help (though he may fake helping) on any other offensive player's drives or perimeter passes.