Currently the Activiti Admin can not be used to audit an instance from start to end as only User Tasks are shown with a started and completed date. Service Tasks and all Service Task sub-types (Document Generation) are only exposed in the Jobs table if they are pending and once completed the are moved out. Request is for parity of the data available in the audit logs be made available in the Admin UI.
Only user tasks are able to be audited in the Activiti Admin
All tasks regardless of type can be viewed in the Admin UI.
Attached is the Audit Log from a process I created with 3 user tasks, a generate document task and a Rest Task. In the audit log attached you can see all 5 steps in the process however in the Admin UI image provided you can only see the 3 user tasks. There is no indication that additional tasks were performed as part of this process instance.