Yes the same thing happens inside Chrome. It is technically not a bug, it is doing the right job, inside the Facebook Developer Console, I have Web as my Platform, and I have a redirect URL to my index.html page for my app. So whenever Facebook login comes up, put my credentials in, and login it redirects me to the index.html page on my web server.
I know this is pointing to my index.html page instead of the Crosswalk export is because I tried to use the action-
On Mobile Back button pressed -> set Text to "It works!!"
When I would export and get my .apk file, I would try it, login through Facebook, and come to the layout where I can press the back button, the text does not change. This is why I know it would go to my index.html page, because the Chrome browser does not support back button.
Now after I have seen it not work that away, I tried a new project inside C2 this time, no Facebook login, and use the same back button action as above, and it worked. The text did change correctly, because I was still running on the export, and not a web page.
So basically taking the Crosswalk app, and ignoring it. I think this is because there is no Native support for Facebook integration with any mobile devices that run C2 apps. CocoonJS, Crosswalk to be the two major ones without native support.
In the developers console on Facebook, you can distinguish the platform, and if you choose Android, you have to give a few things for the Android Facebook login to work natively, these are in this screenshot:
However, even if you added these credentials to the Facebook developers console, there is no way for C2 to use native Facebook integration.
That would be a great addition in my opinion, you open the doors to many new potential projects.