A Service Contract was set up and a Private Service Type was mapped to it.
The affected end user's functional organization to the Service Contract Organization.
When the affected end user is assigned to the Service Contract via functional organization, they only see the R/I/P areas that are assigned to the Service Contract.
Within the Service Contract, there is a private service type, it has only 1 event, based on status being open, but it is not attaching to the ticket.
A Service Contract needs a Private Service Type, that is mapped to a Priority, in order for the Service Type to be automatically attached to the ticket.
Within the Service Contract select the Additional Information tab, then the Priorities tab.
Select Map Priority, then select the Private Service Type mapped to the Service Contract.
Now the Service Type should be automatically attached to the ticket.