Bookmarks are similar to branches (and I believe implemented as branches?) but aren't quite the same thing. In particular, you can't check out a bookmark, you can only check out commits. If you do something like `jj edit <bookmark>`, it'll resolve <bookmark> to figure out which commit it points to, and then check out that commit. If you create a new commit now, the bookmark won't automatically be moved along, because jj doesn't know if you want to add a new commit to the <bookmark> branch, or if you're trying to create a new branch that forks off <bookmark>.
Whereas `git checkout <bookmark>` puts you in a state where you've checked out the _branch_ and not the commit, which means if you create more commits, they'll automatically be added to <bookmark>. To create a branch forking off from <bookmark>, you need to first create a new named branch, then start adding commits to it. (There are other ways as well, but this is the most standard approach.)
The tradeoff with Jujutsu's approach is that it's very easy to create lots of lightweight spin-off branches (just `jj new <fork point>`, no need to come up with names first). But it's slightly harder to do the traditional linear approach where you're consistently committing in a straight line on a single branch, and then syncing that branch with another remote. This is because for each new commit you create, you also need to update the bookmark manually.
In the parent poster's case, it's probably complicated further by them working on the same branch as someone else. Assuming there's no rebasing going on, this shouldn't be too complicated, but it's another case where in git you would check out a branch, and `git pull` will automatically forward you to the head of the branch, whereas `jj git fetch` will just move the bookmark without moving you.
It sounds like the workflow that this person is using doesn't fit that well with how jj "wants" to be used. I believe there's been some talk in jj of a way to automatically update branches when creating a new commit, which would help somewhat, but I think it's also a natural effect of having built their workflow around git, and that flow just not quite working so well in jj.