IANAL and could be completely wrong on this, but I thought a judge would have to issue a temporary stay for them to continue without the threat of some sort of retroactive penalty for violating the cease and desist.

I am lawyer but I'm not sure how the specific laws work. But generally, yes, if a court eventually says that they were breaking the law the entire time they would have retroactive damages. However, I don't think those retroactive damages would stop at the date the AG sent the letter. I think it would go back to when they started to the illegal activity or the statute of limitations.

But maybe NY has some sort of notice rule for this sort of thing.

Interesting, that does make sense from a legal perspective. If you do something illegal you shouldn't need a letter from the Attorney General to tell you it was illegal before you could be punished. Although I imagine that the level of cooperation these companies provide would have some impact on any potential punishment if it were to come to that.

Yes, often the company will negotiate with the AG's office on a settlement. Being cooperative goes a long way.

The letter threatens criminal prosecution as well as civil litigation. If the companies continued while awaiting a ruling they risk company destroying criminal penalties (under the state's RICO analog) and the executives risk going to prison.

Sure, that could have happened even without a letter, but ignoring it is daring them to do it.