When ticket notification plugin is active and user access the control panel, an alert pop-up is shown to allow permission from user to receive notification on new ticket and reply on ticket.
After allow the permission for notifications you receive a subscription message.
When new ticket has been created for user, then user and member of department will receive an notification. When new ticket has been created for staff then staff and member of department and those staff which have permission for all tickets will receive notification.
When reply has been posted on a ticket then ticket user will receive notification.