Okay @SCCPC-AC, I created a "registration required" meeting, registered two attendees, and put them in Breakout Rooms for a few minutes, then back to the main room, then closed the meeting.
In Admin -> Account Management -> Reports for Meetings, there are only three options: Registration, Poll, and Survey. In the Registration Report, this is all it shows:

There is not an Attendance report for Meetings, that I can find. There is an Attendee Report for Webinars... but that won't help you until Breakout Rooms for Webinars is a thing.
Sorry... I think whoever wrote your organization's manual either weren't clear on the details, or misspoke.
There are ways to track who goes where in the API, I believe... but unless you have a class full of programming students willing to take the task on, you're probably not going to get this until someone figures out there's a market for it... then it won't be free.
You could put in a feature request at https://zoom.us/feed.