Ok, there’s nothing that can be done about that, sorry. Here’s why…
You have the directory on the page multiple times under different tabs, which is fine Connections will obviously work, but it is not compatible with the character index because the Connections shortcode is not aware of any other instances of itself when used on the same page or any other instances where it is used in your site.
The character link will only jump to the very first instance of the character group of the character clicked, even if that character group is in a hidden tab. If the very first instance of that character group is in a hidden tab, there is nothing to jump to.
Updating Connections would not fix this and would actually be even less compatible, sort of, because the characters when click will filter the results by the character clicked. The click will cause a page refresh which would mean the current tab would lose focus and every instance of the shortcode would filter by the character that was clicked on all tabs on the current page. The Connections shortcode can be configured to ignore the filtering so that effect can be mitigated on a per shortcode instance, but the page would still refresh and tab focus will be lost even if you allowed only a single instance of the shortcode to be character filterable.
I really hope that makes sense!