Here's a response from our Edge-User's mailing list regarding IPv6 support with Exim:
cPanel intentionally patches Exim to prefer IPv4 over IPv6 when IPv4 is available. The behavior that you are seeing is intentional.
The reason for this is that cPanel has not developed our integration with Exim to be fully IPv6 compliant. In order to do that, IPv6 needs to be raised to feature parity with our tools for IPv4. This includes reseller delegation, reserved IPs, shared and dedicated, etc. Any absence of any feature would be experienced by someone in some configuration as a bug. As we found in an earlier release cycle, our mishandling of resellers and IPv6 caused a few gmail accounts to be blacklisted. We quickly made the decision that it was better to turn off IPv6/Exim and regroup at a later date.
Please do not expect Exim/IPv6 to work. It has not been fully developed and is currently turned off.