At the moment one can choose which applications will send a notification through the Join app on the phone. If you then try to pish the notifications, those that come from blocked apps will not get pushed to the computer.
Non the less, if you try to fetch the notifications manually from the computer, all notifications will appear.
Thus it seems useful to have an option to either block both, or somehow have a list of different applications on the computer. Second option does seem unlikely considering that each device would have different apps.