If you want you can manually add "core.logAllRefUpdates" to the Git configuration, either globally or per-repository.
Just for the record you can also enable Stash audit events if you're interested in
You might also be interested in the following feature requests:
It's something we're definitely planning on adding to Stash at some point.
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG