Email recipients configured to receive email notification for a backup job status receives two notification.
This can happen if under job settings an email recipient is configured and is from a different domain along with an email recipient from same domain where Backup Exec is installed.
e.g.: If Backup Exec is installed on "xyz.com" domain and there are multiple email recipient configured from same domain but one (or more) is from a different domain "abc.com" , then no email notification is sent to the user from "abc.com" but email recipient configured in "xyz.com" domain will receive two email notifications.
Backup Exec uses SMTP for email notifications and supports authentication and Transport Layer Security (TLS).
Notification email messages can be sent to Microsoft Outlook, Lotus Notes, and Web-based email applications, such as Gmail or Yahoo mail.
Remove the email recipient configured from the different domain and then try to test the email notifications
Backup Exec 2012