From the documentation: "Only include tasks that the given user is involved in. A user is involved in a task if an identity link exists between task and user (e.g. the user is the assignee)."
If user is only assignee or owner (or both) of a task, API search does not return this task with parameter involvedUser, although the identity link exists. If I add another identity link of different type than owner or assignee, then the task is returned.

AT:

• When involvedUser is used, filter the query also by task assignee and owner
• Create indexes on those columns
• Validate that it is already correct in the history query (in this case we persist identity links for assignees and owners)