Let's say the cpanel server is located at server1.thewebsite.com but there is the domain thewebsite.com is also hosted on server1.thewebsite.com
MX records are pointing to another email service google/yahoo/etc.
(DNS/MSX is not hosted on server1.thewebsite.com but I have added the same MX records just to see if the server would use them but it does not)
If email@example.com sends a system message instead of the message being routed through the normal path through the external email it only sends it to thewebsite.com main account theweb user.
If an email is sent from another location it makes it to the external email host appropriately.