Upgrading shouldn't be necessary to fix this issue and I don't believe you'd see any difference (regarding this problem) if you did.
There's a few things that would help if you could check in your configuration for Joomla, CB, and JFBConnect. Playing with these settings should fix your issues:
In Joomla's Global Configuration->System tab, set "New User Account Activation" to "No"
In JFBConnect's Community Builder Integration tab, set "Skip CB Activation:" to "Yes"
In Community Builder's, Configuration->Registration tab, try turning "Require Admin Approval" and "Require Email Confirmation" off (if they are already, good)
This should disable all activation of emails and for any users, whether through JFBConnect or registering for a normal Joomla/CB account. If you want to still enable activation for normal Joomla users but not Facebook users, you should just be able to do the first step and 2nd steps above.
Hope this helps.