Weird... let me show you.
See my content fields (I just added Email and Phone):
For example, see the Email settings (with all categories selected):
But then when I'm editing a listing, the content fields are not appearing:
For your information, I create another level (but I don't think is related):
So, I really don't know what's going on... I have the latest WordPress 3.7.1.
Hey! Looking at your demo, I definitely don't see the module "Content fields" or "Listing media".
Something is happening here... do you want me to test something specific for you?