Migration assistant using time machine backup - how long till personal data files show up?

I am setting up a new Mac Mini by migrating my existing data, apps and settings from the old Mini to the new Mini using a Time Machine backup on my AirPort Time Capsule and Migration Assistant via the wireless network router in AirPort.

Everything appears to have gone well in Migration Assistant, but when I now open Time Machine on my new Mini I don't see my personal data files in the User directory on the Mac HDD, neither do they appear in the new Mini's directory tree.

In Time Machine the last full backup date from this morning shows, but it has been "loading" now for > 3 hours.

Question, is this just a matter of my time machine backup files just taking a long time to be transferred over my network (a separate computer (my wife's) is doing a full backup on time machine at the same time, and the time estimate for it to complete was 10 hours or so.