Hi,

If you would like to visible task assigned user wise, then you have to implement security rule in project.task model
such as :

<record id="my_assign_task_rule" model="ir.rule">
    <field name="name">user: own task only</field>
    <field name="model_id" ref="project.model_project_task"/>
    <field name="domain_force">[('user_id','=',user.id)]</field>
    <field name="perm_read" eval="1"/>
    <field name="perm_write" eval="0"/>
    <field name="perm_create" eval="0"/>
    <field name="perm_unlink" eval="0"/>
    <field name="groups" eval="[(4,ref('base.group_user')),(4,ref('hr_payroll.group_hr_payroll_manager'))]"/>
</record>