How to keep tags in sync between two checkouts?

As a test I created a local empty branch. I made some commits and tagged some of them.

When I create a new checkout of that branch, I get the tags from all commits.
So far so good.

But if a tag is deleted in the original repository, the checkout will never see that change.
bzr update will tell me that there's nothing to update. And even if I create more commits,
the tag will never be removed upon updating/pulling.

But a new checkout will not have the deleted tag.

Is that a bug or a feature?

bzr help tag actually tells me that tags should be updated when pulling. So it looks like
a bug to me...