You should only setup the DNS at your registrar to have mail delivered at your server, together with Reverse DNS with your hosting provider (some mail servers reject mail with a non working Reverse DNS),.
To set up your mail server for internal use you need to have a DNS server running on your network, but it doesn't have to be your OS X Server.
In OS X Server the record Jaime is referring to is called a Machine Record, but if you haven't selected the option to Show All Records in the menu (gear) of the Server app's DNS section you will not see any options listed when you click the plus ➕ symbol, but instead will be presented the New Host Name window. An Machine Record actually is an A record.
Try checking just:
host mail.xyz.com
And it will tell you the ip set at your registrar...