Hi there again,
I can see the section you are referring to. This inbox view is not based on the Activiti engine, but it is a virtual view based on document metadata. You can build those views using virtual eFiles, where documents then are searched in the background and displayed to users per folder based on some property values then.
Example:
If the property assignee in the document is set to you, it will be displayed in your Inbox virtual folder, when the underlying template is searching for documents, where the assignee property values equals your user name.
Best regards,
Dennis