The codes change every 10-20 minutes. During that interval, you might be able to figure out whom that code belongs to (e.g. because there's no one else in the room). Then if they test positive afterwards, all their codes from some preceding time interval will be broadcast, you get a warning and if your records of which code belongs to which person are complete, you can figure out who it is.

This doesn't work if the person who got infected was never the only one broadcasting their code close to you.