In our web app, If I use a single browser, login to our application as user A, open another tab and login as user B - User A loses his session data. I assume this is due to
Any major browser will only store one session cookie for a site, but the site developer gets to choose what's in that cookie. It seems like your site is storing user information in the session cookie, which is then getting overwritten when the other tab stores different information in the same cookie.
You don't provide much detail about how your specific site operates, but here are a few general ways of approaching this problem.
1) Use different browsers for different users. Different browsers don't share cookies between them. If your goal is simply to test your site with multiple users, this is the way. You can also use Incognito/Private mode to log in a separate user, as this mode doesn't share cookies either.
2) Don't use session cookies to store user information. This is a non-starter on most websites, but if this is an internal site or strictly controlled environment, you may be able to pass user identification via the URL, POST data, or some other hidden identifier in the request.
3) Store data in the session cookie for all currently logged in users. Depending on the web framework, it may be possible to create a map of user -> cookieData and look up the correct one based on which user is making the request. This is an advanced technique, and I don't actually know if Laravel exposes this level of control.