JFBConnect v4.2.4 is quite old. First, we'd recommend upgrading to a newer release. v5.0.0 is the latest.
As for what's actually happening, your users sound like they have the "Receive System Emails" setting enabled in their profile. This is a setting that can only be enabled in the admin area of Joomla, and not something a user can choose for themselves. That setting should *only* be enabled for users that are meant to receive 'System Emails', like the New User Registration notification.
We've heard of this issue happening in the past when sites were migrated from Joomla 1.5. There are migration tools out there that are incorrectly setting that option for all users. Once set, all users will receive system notifications when they shouldn't. JFBConnect is not the only component that uses the "Receive System Emails" settings. There are features within Joomla itself and other extensions that do the same thing. You'll need to properly set the "Receive System Emails" setting to 'no' for all users that should not be receiving administrator-type notifications.
Hope that helps, but if not, let us know.
Thanks,
Alex