The 'Is active' checkbox will be checked by default when the reminder is created.
For the reminders to be emailed they have to have a send date in the past. The background processing service goes through the reminder tables and looks for reminders that have a send date in the past and 'Is Active' set to true. It then inserts an entry into the tps_user_message tables for that reminder to be sent by email and sets the 'Is active' flag on the reminder to false indicating that the reminder has been processed.
Check the reminders have been created on the Incident, if they have a send date in the past and the is active checkbox is checked then your background processing service may either be stopped or in error. Try restarting the Background processing service in Configuration Center and check the application log on the server running the service to see if it is in error.
Assignment notifications are not handled by the background processing service.