Creating a private task is mainly used to prevent project members from seeing all the tasks in the project.

By default, all project-related tasks are visible to all project members.
If you only want to display the tasks to which the collaborator is assigned/added as a performer, you must deactivate Allow all staff to see all project-related tasks

To do this, go to Settings-> Configuration-> Tasks and define Allow all staff to see all project-related tasks on NOT

If the staff member has permission to view tasks or is an administrator, that member will still be able to see all tasks.