Multiple End Users on Same Device/Browser

Is there a way to control who get’s a push based on the last logged in user session?
Currently, if I log in as Admin then log out and log in as user1 the SID remains the same.

Right now, this push service only works if there is only 1 user per device.

Scenario: Admin logs into website and subscribes to notifications for messages and alerts.
Admin then logs out and another user logs into the same machine.

Now that new user will receive all the alerts for the admin.