How to auto respond to user that ticket is closed?

Glad you got it sorted!

This fixed it, my customers are getting the response back after I close the ticket. 

I just activated the "respond to customers every time a user saves the file" I will see if this works, and respond back.

Do you have Notifications configured in Account-Wide Settings? Apparently you have auto response configured. We don't allow Customers to create Incidents via email but I couldn't imagine that changes default notifications. Have you tested this using a lab service?

Well it is not automatically happening. My users are only added as customers via their email address. They have no login. They email helpdesk and they get the auto response that we put in. But when we close the ticket they are not getting a response back that the ticket is closed. 

Those settings are default. When you RESOLVE or CLOSE an Incident the Customer will receive a notification email. The notification emails contain the entire discussion and most importantly the resolution. This also applies to updates made on the Incident.