The behavior you are describing is consistent with the behavior I experience when I set my lockscreen notification preference to "show all notification content."
This setting has three options:
Show all notification content makes all notifications (regardless of visibility) effectively public.
Hide sensitive notification content respects the new visibility types.
Don't show notifications at all will make all notifications effectively secret.
The option to change your lockscreen notification visiblity is in the device settings under Sound & Notifications > "When device is locked", as shown below.
As Selvin noted in his answer, the option to hide sensitive content is only available if you have set some sort of device lock (such as a PIN or pattern lock). If you can unlock your device with a simple swipe of the lockscreen, this option is not available.