Review option in testcase window does not gets updated accordingly as selected in formal review section

Perhaps I missed something in the use of the term "review option" but if you're trying to establish why the State of the test case doesn't change in accordance with the actions that might take place in the Formal Review section, the update of State is not intended to be automatic.  The approvers and reviewers from Formal Review section do their thing (approve, review) and notifications drive the test case owner to manually update the State as appropriate.

The answer is really that it's up to you.   The only real "flow" through a testcase is governed by the changes you make to State through the Action values (ie ready for review, approve, reject, reopen, retire).   The criteria that drives these state changes is entirely customizable.    If that means a "Formal Review" must be conducted by multiple parties then that is your criteria for moving to the next state.  If that means all "Pre-Conditions" must be met then that's what it means.   This definition can be driven entirely by your (collective within the team) needs.