How to automatically eject external drive after Time Machine runs
Solution 1:
I found a free and useful downlaod that does this:
Time Machine Scheduler
It mounts and unmounts the drive automatically on schedule (and when you boot up, if you ask it to). Also allows a custom schedule other than every hour. It installs a new pref panel to control this. Only downside is that the old TM pref panel does not display everything exactly right anymore -- timestamps are off by a few minutes, it says Time machine is Off even when backups are happening -- but it completely solves the pesky improper ejection issue.
Solution 2:
I have the exact same setup as you, and had the same problem. I would suggest trying SuperDuper, a backup system for Mac's. The paid version includes scheduling, scripting, backup on connect, eject after copy, and more. It also has the ability to work alongside Time Machine, and can create bootable backups.
Solution 3:
You could do a backup using the terminal and eject using the terminal. Then put the commands into a script.