In Admin - Settings - Alerts & Notices, where you have the "New Ticket Alert" enabled, underneath that is a series of checkboxes where you can check who receives the alerts.
Your choices are admin, department manager, department members, or any combination thereof.
So when a new ticket comes in, it's assigned a department (based on its help topic) and then alerts are sent out accordingly to the manager/staff for that department and/or admins.
So it doesn't really matter what any of the system emails are. New ticket alerts will be sent to the email address specified in the user's profile. If your support department manager, for example, has a user account on your system in which he's registered with the email 'bob@somehelpdesk.com' then that's where the alerts for new tickets in the support department will be sent to, if you have "department manager" checked in settings.
Checking 'Admin' sends alerts to the System Admin email address, which you specify in the Email settings (on the same settings page where you set Alerts & Notices).
Checking "staff members" sends the notice to all members within the incoming ticket's department.
