Because this plugin is only triggered on word characters (let l:kw = matchstr(l:typed, '\w\+$')), if a string is entered that contains hyphens, for instance, tags aren't searched.
Would it be possible to re-implement g:asyncomplete_default_refresh_pattern and use that?
Otherwise, I'm finding that this works much better:
let l:kw = matchstr(l:typed, '[[:alnum:]_-]\+$')