WordPress already provides a very nice API for admin / option page tabs. No need to reinvent the wheel on that one.
Your Ajax action is “options.php” You need an action that’s linked to a PHP function that gets included by add_action( 'wp_ajax_YOUR-ACTION-NAME*', 'your_php_function');
* YOUR-ACTION-NAME is the action you defined when localizing the script
Take a look at Chip Bennet’s very detailed tutorial on the Settings API. It covers just about everything including tabs.
There is also a lot of great information here-> ajax on WordPress Ajax.