Issue okta login with Local storage

HI Team,
i am using react with dotnet and okta react client v3.0.7 , we initiate the okta login when the user types http:localhost/oktaTest url then the user is authenticated by okta and getting the access token every thing working fine , then the user clicks logout button on button click event we are clearing the local storage so every things work fine .
if the user is not click on logout and close the browser and open another instance of browser types http:localhost/oktaTest URL then the user is not authenticate by okta because there is already data exists in local storage we wrote a code when the user is close the browser with onbeforeunload but its not working in all browsers , can you please shade some light on this issue ans please suggest any solution .

@phani Hi,
Okta uses an HTTP session cookie to provide access to your Okta organization and applications across web requests for an interactive user agent such as a web browser. A session cookie has an expiration configurable by an administrator for the organization and is valid until the cookie expires or the user closes the Session (logout) or browser application.
For more details, yon refer the doc

Can you pleas clarify your your use case? Do you mean closing browser does not help you clear local storage? And what is the functionalities of your workaround?