Very few three person games here in all-IAABO Connecticut, but I'll give it a shot.
First, all dead ball movements of officials after a foul, while the foul is being reported, are referred to as
switches, not rotations.
Rotations are movements by officials (often during a live ball) to gain better coverage, usually initiated by the lead moving across the lane, with trail and center rotating their positions (while staying on the same side of the court).
For switches as fouls are being reported, the official reporting the foul will always go opposite the table. If he originally came from opposite the table, he goes back there and nobody else switches.
If the calling and reporting official came from the lead, the official opposite the table before the foul switches to the new lead. Third official stays put.
If the calling and reporting official came from the table side center, or trail, the official opposite the table before the foul switches to the table side. Third official stays put.
If you're not the reporting official, and you're opposite the table as trail or center, just think, I have to make room for the reporting official to rotate into my position, where did he come from because I have to replace him.
As usual, check your local listings.
Keep in mind that this is coming from a person who has worked fewer than a half dozen three person games in thirty-seven years, so take it with a grain of salt.
