Textmate automatically updates any bundle you select in the bundles pane of the Preferences window (about 100 bundles there).

If you’re using personal bundles that live on git, Textmate can’t know how to access those for updates, so it’s up to you.

It's not like there's no way to tell TextMate where to fetch the update from. It's just that Allan did not implement any logic for those autoupdates for non-official bundles.

For example Safari can autoupdate extensions downloaded from github easily by reading the plist file that has all the data necessary for the autoupdate to work.