When tickets are closed in Process Manager the tickets are changed to the closed status but are still seen in the My Queues assigned queue.
The My Queues web part is populated by a report (My Queues) that is set up to show all of your tickets regardless of status. You can edit this report if you'd like and filter out the status types you don't want to see. When you edit the report, on the left hand side of the editor you will want to click on the Status option. It will then open a box to allow you to specify which statuses you wish to include or exclude. Then they just save the report.
Note: The My Queues report is built to show open tasks for incidents in assigned queues and not the status of the ticket. If closed tickets have active tasks the incident will show up in My Queues and to clear these out the active tasks need to be resolved.