By default, all project-related tasks are visible to all project members. If you want to show only the tasks where a staff member is assigned or added as a follower, you need to turn off Allow all staff to see all tasks related to projects.
To achieve this, go to Setup → Settings → Tasks and set Allow all staff to see all tasks related to projects to NO.
If the staff member has permission to View Tasks or is an admin, they will still be able to see all tasks.