Always add domains in pairs, with and without www. Redirect one version to the other version. Check the "wrong" version periodically to make sure nobody is linking to it. Most other things will be the same.
However when I check GWT for domain example.com and click on "Links to your site" it lists example.net as being the site with most links to example.com.
There is nothing to fix here - this is how GA reports it when you have 301 redirect. What you have done is fine. Every now and then do go and check example.net domain to make sure there are no issues there.