If your domain for example is pointed just via A record to your Server, you shall not be able to send mails from the servers because the MX records are pointed elsewhere. You can easily change that just by log in via SSH on your dedicated server and then open:

/etc/localdomains

If the domain is listed here and remove it if it is. Next you should open

/etc/remotedomains

And add the domain here. Now you shall be able to send mails from the server with that domain