We were waving iPhones feet away from the tag. It didn’t get picked up so we wandered out to the neighborhood.
My guess is, to preserve battery, iPhones wake up and scan for nearby AirTags only X seconds at a time (don’t have actual numbers, but guessing somewhere between 30-120 seconds). Whatever AirTag ID they pick up, they send anonymously to the cloud along with location. If the owner has the tag in lost mode and the ID matches, they get notified.
This means if you’re walking around with your phone and it hasn’t hit the scan window, you could miss the tag. This works in a high-density area like a city center with lots of phones waking up and scanning at different times, but not so much in low density places.
In that case, a GPS tag with cell modem might work better, but it’s a lot pricier and requires regular charging.