When you're the clock operator without any audio communication to the on-field crew what should you be doing when you get a start the game clock signal (wind) when you should be getting the on the snap signal (chop)?
ANSWER: You do as the on-field crew instructs. If they instruct you to start the clock incorrectly, that is on them. As Kalle offered, note the time when this happened, in case you need to defend yourself. A great CO would also be noting the time every time the game clock is stopped, so, as you are trying to alert the crew via O2O (if available), you can go ahead and start the clock as instructed. Then, when/if the on-field crew recognizes their error, they can order the clock to be stopped, and have you re-set it to the last time it was stopped. They'll thank you.
But, let's back up to the first play. If the situation was less than 2 minutes remaining in the 2nd or 4th period, then, yes, the game clock should start on the snap, even after the offside with contact penalty (due to the BC out of bounds on 1st down). Otherwise, in NCAA, the game clock should correctly be started on the Referee's signal following a BC or loose ball out of bounds, irrespective of the offside penalty.
Robert