Their support page is bogus to boot.
The only iPod song trasfering I can find mention of is the ability to take songs dowloaded in the app and move them to the iPod app. They tell you to use File sharing, which means that while their claim isn't exactly a lie, it's not really a direct trasfer feature either. Here is a link on how File Sharing works.
iOS: About File Sharing
Basically what you would have to do is use the File Sharing feature in iTunes to copy them to you computer. Once ther you can import the files back into the iTunes library, the same way you would import any music track (using Add to Library under the Files menu). At that point it would be available to sync back to your iPad and show up in the iPod app. Or you could sync it to any other iDevice you own.