Wordpress automatically do the login after registration

I'm new to wordpress. I'm modifying a plugin that create an ajax form to register a user. After registration if I refresh the page the user is automatically logged in. I don't want it (I need to send a random password to verify that the user read the email message).

I have tried to add

wp_set_current_user(0);
clear_auth_cookie();

after the user registration but nothing change.

What can it be?

Here is the function that receives the POST message from the form:

function the_do_login()
{
    if($_SERVER[ 'HTTP_X_REQUESTED_WITH' ]=='XMLHttpRequest'){
        if ( $_POST['the_form_action'] == 'login' ) {
            // user already registered,
            // do the login with wp_signon
        }
        elseif( $_POST['the_form_action'] == 'register' ){

            if ( !empty( $_POST['user_login'] ) ) {
                // check the user name..                    
            } else {
                // error on user name
            }
            if ( !empty( $_POST['user_email'] ) ) {
                // check the password..
            } else {
                // ....
            }
            $user_data = array(
            'ID' => '',
            'user_pass' => $password,
            'user_login' => $username,
            'display_name' => $username,
            'user_email' => $email,
            'role' => get_option('default_role') // Use default role or another role, e.g. 'editor'
            );
            $user_id = wp_insert_user( $user_data );

            // instead of wp_new_user_notification generate a random password and send it to the user
            wp_new_user_notification( $user_id, $password );

            echo '<div id="login_error">'.__('Your account has been created and an email is been sent to '.$email.'. Check your email to confirm registration').'</div>';

            wp_set_current_user(0);
            clear_auth_cookie();

            die();
        }
        elseif( $_POST['the_action'] == 'reset_pass' ){
            echo do_action('login_form', 'resetpass');
        }
    }else{
        wp_redirect( home_url() );
        die();  
    }
}