OK... things seem to be behaving in the desired way.
I was afraid that I would have to do a full backup of the disk. I ran the backup anyway.
What happened was that I had some weirdness with the backup volume. It complained that it didn't know where it was. I browsed to my regular volume for this backup it and things started working.
The system scanned the disk and figured out that it was the same and only backed up changes since before I extended it.
It's all good now, but the behavior is a bit confusing.