When you order a domain name through our service, we have you make a payment to Escrow.Com, the number one Escrow service on the internet. These are the same folks who handle Ebay and Godaddy, among other big names.
Once Escrow.com receives your payment, Premium Domain Names then transfers the domain name to you. Escrow.com checks to verify that the domain has indeed been transfered and is now registered in your name. Then and only then wil they release the funds to us.
Now, you are the official owner of the website.
To learn more about this (though we pretty much covered it all) go to Escrow.com and click on domain buying.