I don't think there is a way to get TM to back up Automatically when the hdd is connected, I use an external but it's not always switched on, i just gor to TM prefs and back up now, No biggy and jobs done.
If you follow these instructions, it will re-format your disk so TM will have to do another "initial" backup which will take a few hours.
But this may fix your problem. TM does do backups automatically.
The other question I have, is when you plug in your drive and it mounts on your desktop (or side panel in a Finder Window), do you wait a few minutes for TM. Sometimes TM waits a few minutes before starting an automatic backup.
The other question I have, is when you plug in your drive and it mounts on your desktop (or side panel in a Finder Window), do you wait a few minutes for TM. Sometimes TM waits a few minutes before starting an automatic backup.