The closebrackets addon has a bunch of scary heuristics to try and decide which behavior is appropriate when. I think you were typing the bracket right in front of the closing quote character, which was indeed not working. I’ve adjusted the code in this patch to fix that.
If that was not the problem you were having, let me know. (Autoclosing when typing inside of or before a word intentionally does not work.)
PS thanks for posting the first real question on here!