After adding a new domain, it says Subdomain added, what to do?
There is nothing to worry about, cPanel calls your addon domain a subdomain because the root directory of your addon domain is inside your primary domain's root directory (public_html). The functions of your new domain will be completely same as your primary domain, so there is nothing to worry about.
If you want you can create the root directory of your addon domain outside of public_html directory like public_html_addondomain, etc. With this you can make sure your visitors can not access your addon domains.