SharePoint 2013 Publishing Site
When using multiple URLs for site associate the public URL of your website with the Internet Zone.

When extending Web Applications you can define up to five URLs associated with five Zones. This mechanism has been available since SharePoint 2007. In the previous versions of SharePoint the Zones were nothing more than labels and it didn’t really matter with which one the public URL of your website was associated.

In SharePoint 2013 things are a little different as some of the new capabilities, such as XML Sitemap, expect the public URL to be associated with the Internet Zone. If you are using multiple URLs with your website (either if you are using Alternate Access Mappings or SPSiteURLs with Host-Named Site Collections) you should ensure that the public URL is associated with the Internet Zone if you want the new capabilities to work correctly.