Alt+` (key above tab on most keyboards) should allow you to switch between windows of the same application. So you do alt+tab till you get to your browser, then alt+` to pick the right browser window.
Alt+Tab is usually bound to "Switch applications", which means all of the target application's windows come to the front, possibly sending every other application window out of view.
Sometimes a more direct approach is to use the action "Switch windows" by assigning it a shortcut Keyboard settings.
Sometimes a more direct approach is to use the action "Switch windows" by assigning it a shortcut Keyboard settings.