They took her to the dog park on 5/9, and got the notification that an AirTag was following them. So I was gone for a little over 24 hours, but they only got the notification after they took the leash with them for a couple hours and then went home.
I believe the 3 days is for the audible beeping when it's moved, but they haven't seen that yet and they marked it as "pause safety alerts" so I'm not sure if it'll still beep.
Edit: Also, I have a bag at home with an AirTag and it's constantly updating location, so presumably one of my neighbors has an iPhone that's nearby. Kind of cool that it updates so frequently, and I'd say it was worth replacing my Tiles because of it.