In WHM Advanced Exim configuration editor or via SSH /etc/exim.conf.local
change the ROUTERSTART
From something like this:

send_to_smart_host:
driver = manualroute
route_list = !+local_domains dedrelay.secureserver.net
transport = remote_smtp

To this:

send_to_smart_host:
driver = manualroute
route_list = !+local_domains dedrelay.secureserver.net
transport = dkim_remote_smtp

Notice the important part is not whether DKIM auth keys have been generated, added to the DNS and is activated via WHM and configured in your Cpanel, but whether the default transport setting is actually configured to use the DKIM