avopolis Hi
It's a weird issue as I tried to assign to Cassiopeia template - a standard template of Joomla but the unpublished article still shows there, it means that the problem is not from JA Comics template. I'm trying to find if there is any special setting but not found it yet.
Normally, the unpublished article can be seen (on frontend) by Super User group only. So I guess there is something wrong related to the permissions or any 3rd party extension. You can assign that page to Cassiopeia template and see the same.