I think the issue is the server can only send one response per request, try using ajax. I'm haven't used JSF very much but that might help. When you make a request the server can either send the download back, or the refreshed page. With ajax you can have a request be made to update the count, separate from the download request.
It looks like by saying response complete you cancel the page from being loaded, which you are correct by doing, because if you didn't the user would download part of the page with his file.
If you have a javascript function that makes an ajax call to refresh the counter when you click download, that might work.