Is This Correct Setup?

Hi all,

I have a wordpress multisite setup for people to register blogs/websites as subdomains (Creativ3Sites.com). I have a question regarding this plugin and it's use with one of my clients. Here is a simple walkthrough of what I am trying to accomplish.

1. I have a client who has an account with us. Their domain is theglobalbulletin.com.
2. They are wanting to have subsites of their website (i.e. map.theglobalbulletin.com, news.theglobalbulletin.com, etc.) so they can have different themes for different parts of the website.
3. I currently have domain mapping configured on Creativ3Sites.com where the client is currently hosting just theglobalbulletin.com

Is it possible, with this plugin, to allow what I have described above? Where the client can create subdomain sites of their website through my multisite network? Do they need to have their own hosting account?

What I have done so far is taken their domain hosted at GoDaddy and added a * under the A records pointing to my dedicated IP Address. I'm assuming that this will work but I am not 100% sure.

I then have the domain under the setting > multi-domains. Do I need to set this to private? I only want that client to be able to access creating sub sites of theglobalbulletin.com. If so, how do they create their own sub sites with the private or do I, as the Super Admin, have to create each of their sub sites?

Any feedback would be greatly appreciated. Thanks!