When you release the trigger on a chainsaw, how quickly should the chain stop?

Fairly quickly but 1 second would be totally normal. If it was stopping immediately, the likelihood is that the chain tension was extremely high.

If the saw is adjusted properly, the chain will stop immediately when you let off the trigger if there is resistance against the chain. This means that when the blade is in contact with wood and you stop pushing the trigger, the blade stops immediately. If you are reviving the saw and the chain is not in contact with anything, it might continue for a revolution or two but it would stop if chain came in contact with something.

If the blade is turning when you are not on the trigger and in contact with wood (it would likely be moving slowly but this is still dangerous) then the idle on the saw needs to be adjusted.