Facebook doesn't allow some of their widgets to be used when you're in the "Use Facebook As" mode and have selected to be a "Page". Since any user can create unlimited Facebook Pages, those Pages can't have the ability to Like content from websites. If so, it'd be immediately abused to inflate Like counts.
So, when you're in the "Use Facebook as Page" mode, and you visit your site, that ugly little box will show up. When clicked, it will ask you to switch accounts to your personal profile instead of the Page that you are logged into.
Unfortunately, there's nothing we can do in JFBConnect to bypass or alter this behavior. That's how Facebook works.