The thief will be notified of the tag in less than an hour usually. I see the alert anytime I mind my friends dog. Typically within 45-60 minutes of my friend leaving, I get an alert which includes a map of where I was tracked and my friends email address.
The original Airtag use case included theft but you'll notice any mention of that has now been removed from the marketing material. It's really just for people who lose things.