The logic to fetch or create data for TouchUI inbox is not at the front end as in case of classicUI but 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 [1] which creates the html page per [2]
At the same time [1] triggers a get request to fetch the data for the inbox page [3] which is handled by a servlet [4] and used by [2] to create the complete inbox page
Further on logic goes to [5] and [6] to fetch the data per the logic
[1] /libs/cq/inbox/content/inbox/jcr:content/views/list/datasource
[2] /libs/cq/inbox/gui/components/inbox/inboxitem/list/list.html
[3] cq/inbox/gui/components/inbox/datasource/itemsdatasource
[4] com.adobe.cq.inbox.impl.servlet.ItemsDataSourceServlet.java
[5] com.adobe.granite.workflow.core.WorkflowSessionImpl.java
[6] com.adobe.granite.workflow.core.jcr.WorkItemManager.java