It seems like everything is setup properly.
There is a script in your osticket /upload/ folder that you need to run as a cron job.
What's happening when you run this as your web server user?
/usr/bin/php /var/www/osticket/upload/api/cron.php
It's possible that your cron.php file is somewhere else. Just find it and give it the right path.
Does it fix your email fetch issue?
J