One of the common requests we get from new users of Domain Mapping System is to secure the secondary URL that is mapped to a website.
In order to do that, you'll need to generate an SSL certificate for each domain added to your server.
Many hosting providers will offer free SSL certificates that renew automatically for all the domains. cPanel now has an "Auto-SSL" feature built-in, which should include any domains added via cPanel:
For more information, see the relevant cPanel documentation.