If you set up Minimum quantity of referees for Referrer rewards, you should set up 2 emails of Successful referral: When referrers referred enough referees and when not.
When customers referred enough referees
When customers did not referred enough referees
Others
Referral invitation
Reward expiry reminder
If you set an expiry date for referrer or referee rewards (the discount will expire after X days from the created date), you should enable the Reward expiry reminder email.