Notifications don't go to your computer they go to your eMail address. If you have eMail settings set up on your computer that is why they appear to go to your computer.
Turning off notifications in your communication preferences will result in receiving no notifications to your messages. Leaving it on you will get notifications both in your messages and your eMail address or just to your eMail.
I have notifications turned off so I only receive eMails regarding purchases nothing comes through messages.
