Alright, I've solved it myself.
As stated before, the documentation was really not good. Here's the solution for anyone who wants to integrate this code in future
Firstly, you have to make your baseurl like this in config.php
"base_url" => "http://yoursite.com/subdomain/index.php", OR
"base_url" => "http://yoursite.com/index.php",
Note that I'm not using www. Don't know why, but it does not work with www.
Now the tricky part, you have to include this in your index.php file
require_once( "PATH_TO_HYBRID/Auth.php" );
require_once( "PATH_TO_HYBRID/Endpoint.php" );
if (isset($_REQUEST['hauth_start']))
{
Hybrid_Endpoint::process();
}
The Endpoint Process is what makes you redirect to a blank page if not provided. And you must add it to the index.php as far as I've tested.
Now the code should work fine :) I'll be happy if it helps someone.