I just got a mac mini and time capsule. I set it up for my family with multiple user accounts. I was confused that the backups didn't work when I logged out. If your logged out your not making any changes but if you made a change and then logged out, you would want that backed up.
Anyhow, I think the solution is simple. Don't log out. Use Fast User Switching, this leaves you logged in. I haven't tested it but one of the options is the login screen on Fast User Switching and I suspect it leaves you logged in and all your processes running.