How does Apple (privately) find your offline devices?

I quote from the article:
How is this system going to avoid being a massive privacy nightmare?
The good news is that Apple claims that their system actually does provide strong privacy, and that it accomplishes this using clever cryptography. But as is typical, they’ve declined to give out the details how they’re going to do it. […] an incomplete technical description that Apple provided to Wired […] provides many hints. Unfortunately, what Apple provided still leaves huge gaps. It’s into those gaps that I’m going to fill in my best guess for what Apple is actually doing.