That is the current current functionality. The character index does not filter by character or jump to the page that the character group exists. The links only jump to the character group if it exists on the current page. The premium templates use to filter the character index to show only the characters that existed on the current page of results; but so many requested that all letters be shown regardless of the fact that when clicking a character would not jump or filter the list by the character that was clicked. So, in the last updates to the templates I removed the filter. With that said, later this summer, the character index will receive an update so the it will filter by character as it does in the admin.
Hope that helps.