That setting should not affect the ability to authenticate - you shouldn't really enable that option unless you're debugging something.
Just as a recap, there are two types of SMTP relay authentication on cPanel servers:
1. SMTP AUTH where the client uses their cPanel account username and password in their email client to authenticate as they relay email through the server
2. POP Before SMTP where a client must POP their email account within 30 minutes of trying to relay email through the SMTP server
The POP Before SMTP process is controlled by the antirelayd process that runs when you (re)start exim. So, the first check is to make sure it's running OK:
service exim restart
If antirelayd doesn't or wasn't running, ensure that both tick boxes for it are enabled in WHM > Service Manager
Secondly, the antirelayd process detects the POP logins by tracking the information shown in /var/log/maillog, so you need to ensure that that file is actively being updated with the POP logins. If it isn't, then you're probably suffering from the /tmp noexec bug in logrotate:
http://www.configserver.com/techfaq/index.php?faqid=38
If that's the problem, restart syslog:
service syslog restart
That ought to cover all aspects of SMTP relay authentication for email clients.