The CCS (Calendar and Contacts Server) calendar can send invitations, it just doesn't happen automatically. Additional steps are required to send invitations. The default/native Webmail calendar, however, sends invitations immediately after the event is created without any further steps.
This bug is known to cPanel and an internal file has been opened in this regard (CPANEL-41540) for their development teams to investigate this issue further.
As a workaround, while waiting for this bug to be resolved, you can click on the event you've created, then select Options. Then select Send. This will open Roundcube's Composer section, allowing you to add recipients and, if you wish, a body. Once you've sent in this compose section, invitations will be sent with a calendar attachment (.ics file).