For workflows it is medium by default. You can change it though in process step using WorkItem API.
The logic to fetch or create data for TouchUI inbox is at the Java side, below is the basic flow:
~ A request to '/aem/inbox' resolves to path '/libs/cq/inbox/content/inbox'.
~ This renders data per  which creates the html page per .
~ At the same time  triggers a get request to fetch the data for the inbox page  which is handled by a servlet  and used by  to create the complete inbox page.
~ Further on logic goes to  and  to fetch the data per the logic.