In that case you need to echo the JavaScript on the final page as currently (as suggested above) the page is redirecting before the JavaScript is seen by the user.
You need to send back a message to contactus.php which allows you to tell the difference between a successful and failed message, you can do this with a query string (?name=value).
Then you must place the javascript code on contactus.php
Alternatively you can use an AJAX request to send the data to contact_us_action.php and put the alert() code after the AJAX request was succesfully completed.
However. I must tell you that users generally dislike the little popup boxes on websites. It’s better to create a different form of feedback.