Issues with relay server connecting to Mailgun

What I'm trying to do: Send out Wordpress notifications using SMTP/Mailgun instead of PHPmailer.

• I have a production VPS with one IP and several Wordpress installs with different domains. The mail port for it is blocked so I had to create a SMTP relay server using exim/dovcot.

• The SMTP relay server is using exim/dovcot as well.

Currently Wordpress is able to send out emails using PHPMailer and the relay is working fine, but I'm unable to send WP notifications to Google Apps.

I'd rather use a service like Mailgun to receive emails from Wordpress and then send them out through Mailgun to whomever they need to go to for each domain using a subdomain.

Currently I have the required dns setup with mailgun and the subdomain is validated. I setup the TXT, CNAME and MX records. I have the mx records pointing to my subdomain.

Is there anything I need to setup or change with either of my servers to allow SMTP to work with Mailgun?

Is there anything I need to change in WHM / Cpanel

Domain Verification Screenshot

via Chebli Mohamed