It uses bluetooth, at least thats what it says in the description. I think when you are close to the tag, it saves the position. It gives you alert when you are leaving it behind; the range of bluetooth is ten meters/30 feet. And as long as someone don't move it, the position will be the same and the app can measure the distance. Just like you've said. :)
How it works:- Put Nokia Treasure Tags on your favorite belongings
- Connect tags to your phone via Bluetooth Smart
- Your phone alerts you if you’re about to leave something behind
- Audio alerts mean you can use your phone to find a tag, or a tag to find your phone
- Maps from HERE service and LiveSight-compatible phones let you use augmented reality to find your belongings
- Pin your favorite tags to Start as live tiles for quick access and status updates