This is my logout.php script. It's just supposed to delete the cookies so the person is not longer signed into the website. It's getting through the script, because the redirect is working, but the cookie is still there if I reload a page where its value is displayed.

Code:
<?php # Script 7.4 - logout.php

// If no cookie is present, redirect the user, else delete the cookies.
if (!isset($_COOKIE['cust_first_name'])) {
	header ("Location:  http://" . $_SERVER['HTTP_HOST'] . dirname($_SERVER['PHP_SELF']) . "/index.php");
	exit(); // Quit the script.
} else { //delete cookies' values
	setcookie ('cust_first_name', '', time()-300, '/', '', 0);
	setcookie ('user_id', '', time()-300, '/', '', 0);
}

$title = 'Logged Out';
//HOME, ABOUT, LOGIN, SIGNUP
$cat = 'LOGIN';
include('./head.inc');

echo '<script type="text/javascript">
<!--
window.location = "index.php"
-->
</script>';

include ('foot.inc'); // Include the HTML footer.
?>