Sorry for the delayed response in getting back to you.
There's not a way to automatically add the FB Comments box to the bottom of your video extension like we have for K2 or Joomla content. However, there are a few options that you can use to add it to your page:
1) Use the SCSocialWidget module, which lets you configure any social widget (like the FB Comment box), and set it to display on your JUserTube pages. That works if you have a specific menu item for JUserTube items or if you have another extension that would let you configure the module to show when that component is loaded.
2) Modify the JUserTube templates to add the Comment box. All you'd need to do is add the following 'tag' to the JUserTube layout file:
The big thing is figuring out where to add that. You may need to contact their developer to get the right information on where and how to add it.
I hope that helps explain, but should you have any other questions, just let me know.
Thanks,
Alex