The category select pagination issue is not the same. The fix for that is included in the latest releases.
The character index works only for inpage links where the character group that is clicked must be on the same page. If the character group is not, the link will not do anything.
Previous versions of the template filtered the character list to show only those characters that are found on the current page of results. Do to a large number of requests to show the entire character index, I removed the filter. I did explain in each request that clicking the character would not take the user to the page or filter the results by the character clicked to those requesting it, but that didn’t seem to matter for their use.
Any way … sometime this summer the character index will receive an update where it will filder by the character clicked. I say I am about half finished with the feature as it is already implemented in the admin manage page.