My understanding is you should only get the notification if the tag isn't with its owner. That's how it plays out in my personal experience. Back when AirTags were completely broken and didn't support family sharing, I'd get notified if I had my wife's car keys with me only when she wasn't with me, i.e. because I grabbed hers to run a quick errand.
This notification would be utterly useless if that were no longer the case: you'd spend half your time on a flight or bus ride closing the unwanted and unhelpful popups.
This notification would be utterly useless if that were no longer the case: you'd spend half your time on a flight or bus ride closing the unwanted and unhelpful popups.