If your domain is using external mail server ( Google mail ) for its pop and smtp activities, you need to make the following changes in your cpanel server.
REMOVE the domain from /etc/localdomains
ADD the domain to /etc/remotedomains.
Finalyl restart exim , Check via the following command to send test email.
sendmail -v “firstname.lastname@example.org”
sendmail should connect to google mx records.