We're going down the rabbit hole here... It seems the App Verification box is checked green, until you fill in details about the user_managed_groups field.. then it adds that "Page for Testing" prompt, which I think is an error. I didn't notice that in my testing yesterday.
First off, instead of user_managed_groups, they just added a new permission "Groups API" that you should be submitting instead, per this footnote:
developers.facebook.com/docs/facebook-lo...-user_managed_groups
Even when you request that permission though, you'll still be asked to provide a Page.. which doesn't seem necessary.
I've submitted a bug on your behalf about this. Facebook is inundated with support right now.. they're responsive, but not as quick to actually fix things. Here's the report for your app:
developers.facebook.com/bugs/166049687403115/
The other option is to actually add a Page Tab to your Facebook Page. JFBConnect should automatically setup the Page Tab info, so you just need to add the Tab to any Page you administer. Then, you can fix that setting in the review and hopefully proceed. To add the Page, go to the Page Tab/Canvas admin section in JFBConnect. At the top of the Page Tab section, you should see:
Your Page Tab application appears to be setup properly. To add it to your Facebook Page, Click Here.
Use that click here link, add the Page Tab, submit the review. Then, you can likely just remove the Tab from your Page since it's not really needed.
Whew... good luck!
Alex