In HappyFox, when a ticket is created and unassigned, it sends email notifications to all the staff associated with that particular category.
Once a ticket is assigned to a particular staff, the email notifications are sent only to that respective staff. If some other staff participates in that ticket, either by adding a private note or adding update to the end user, he/she will also start receiving email notifications.
You can manually subscribe to a ticket, by clicking on the star symbol on the ticket snippet. A particular staff can add other staff members to the subscribers list using "Add Subscribers" option in the "Add Update" area.
In general, email notifications are sent to assigned staff, participants(who has added private notes/update) and subscribers.
Also, make sure under My Settings >> Notification preferences, all the notification options are enabled for staff to receive notifications.