Setting up a sub domain

I was going to release subdomains for people to use.

eg their_site.mydomain.com

Have added "their_site.mydomain.com" as a new virtual server

and added as a server within "mydomain.com"

Both options seem to work. However if they are a server within "mydomain.com" when they login they get access to "mydomain.com". Not what I was after.

But it is would be neater if the subdomains were nested.

What are experienced users doing? Which is the preferred path?

And would there be an advantage to creating a subdomain differently to a full domain? The CPanel server I am using now has then as two separate issues?

Sorry to keep up the posts, hopefully I will get up to speed soon and be able to contribute myself to the community.