Setting up a smarthost when you use cPanel will require that you drop in and do a little configuration of exim. This info should work (but please do be aware that there are many different versions and variations of cPanel - if this doesn't work, let us know at firstname.lastname@example.org).
Create a file /etc/exim.conf.local
Put these lines in the file
driver = manualroute
domains = !+local_domains
transport = remote_smtp
route_list = * outbound.mailroute.net
Next run the below command to activate the changes.