The recommendation to use www is completely taken by how you're accessing your admin area. If you go to your admin area as
site.com/administrator, Autotune will recommend non-www URLs. If you go to
www.site.com/administrator, you'll get recommendations with www. So, if you want www URLs either:
* Edit them yourself it Autotune before setting them and adding www
* Go to the admin area of your site using www and hit Refresh to get new recommendations that should include www.
Hope that helps,
Alex