Our agents do not want to receive any ticket update notifications to their direct email addresses. How do we stop emails going to our agents' personal emails?
Email notifications for ticket updates are controlled by the triggers listed under Admin () > Business Rules > Triggers.
To disable email notifications to your agents, deactivate any triggers that have the action of Notify assignee" or "Notify group" in them.
Be careful not to deactivate the two default triggers with the action of "Notify requester", as this will prevent any email notifications from being sent to your end-users for updates to their tickets. More information about each of the default triggers and what they do is available in the article, About the Support default triggers.
For more information on triggers in general, check out the following resources: