Hi,
Thank you for the details!
The list only displays the first post type name associated, it is a visual thing only, it will still apply to all post types assigned with the taxonomy, you don’t have to worr about that.
I tried to log-in to quicky look at the settings, but the username/password is not working unfortuantely. Can you please check that?
The post type filter seems to be working okay, that is a very good sign, so this is very likely only a minor misconfiguration.