I trigger Jenkins from a post-receive hook on my git server:
curl -s "${jenkinsUrl}/git/notifyCommit?url=${cloneUrl}"

When I push a (annotated) tag on the latest commit that Jenkins has already built, no new build is started.
Since the commit sha of the branch to build doesn't change that's logical.

However, since I use 'git describe' to provide traceability of my artifacts, this is not what I'd like to happen: the 'git describe' output actually changes because of the new tag.

To fix this, the git plugin must not only look at the commit sha but also check the tags on the latest commit that it has built; if there is a new/changed tag on that commit, a new build has to be started.