I had the same issue and solved it changing line 82 of filedownload.php
from
$filename = WP_CONTENT_URL . '/'.$file;
to
$filename = $file;
I don’t know if this breaks any other functionality or something, but at least the counter works now. Maybe this part of the code needs some detection as to whether an absolute or a relative link is given. I used an absolute link and the counter didn’t work on the frontend, but did work on the backend (what Op described).
