This page explains how you can secure a WordPress website domain with an SSL certificate.
When you point a domain to a website hosting server, that server needs to have some kind of SSL certificate installed on it in order for the website to be secure.
In the case of Domain Mapping System, you'll have multiple domains pointing to your server and WordPress installation. By default, hosting servers will generally support securing the primary domain registered on the server out-of-the-box.
Once you've added an Alias domain to your server, you should be able to generate or add an SSL certificate for that domain, which is necessary to secure each domain.
For more information about securing multiple domains on a single hosting server, see this documentation: