why big ip needs to access hosts of vlan for which it ask a self ip.

maybe you're confusing data-plane and control-plane. self-ips and vlans resides on the data-plane, it handled by tmmd(bigip traffic management daemon, in short). tmm caliculates nat, snat and floating objects etc... and the management-ip resides on the control-plane, it handled by linux ( generic ethernet0). Load balancing algorithms will run at data-plane only, not the manamement segment(control-plane). so, looking at your diag, you have to create one more vlan and self-ip, then deploy a client on that segment.