From a retired college basketball official acquaintance of mine. NOTE- He never called Big 10 games:
“Your question is not easy to answer. You are assuming there are specific rules that govern every possible scenario, and there isn’t.
“I have not seen the replay, but to your point, Illinois was not out of line for standing anywhere on the court. That is not an official deadball timeout, and honestly, it sounds as if the officials should have been involved sooner.
“If the Wisconsin coach made contact with an Illini player, and if I had seen it, I would have run him. Would not have mattered if it was the start of the game or the last seconds. Now, that is me. Yes, some officials would not do that if the outcome was still in question. A coach never touches a player. Period. Especially an opposing player.
“You said a double technical was called. As you have presented it, I don’t understand why the Illini player was assessed a Technical, other than if the official did not want this situation to dictate the outcome. Double technicals are typically left for players.
“Finally, if there was contact, expect Illini coaches to send in the tape with their review. At a minimum, the Wisconsin coach will be suspended for a game and most likely receive an undisclosed fine.”