No need of jQuery, simple javascript would do this.
Code:
var logout = confirm("Do you really want to Logout?");
if (logout == true)
{
window.location="*yourplace.com/yourpage.php";
}
Now put this under a function say confirmLogout() and call this on onclick event of button.
Now on that PHP page, where you'd redirect destroy the session etc. and whatever you want to do and redirect it to homepage at last.
For eg.
PHP:
<?php
ob_start();
session_start();
session_destroy();
header("Location:homepage.html");
?>