WordPress: Scheduling an event on form submission

I’m working on an application in WordPress, and I want an event to be triggered when the user submits a form. I have scheduled an event using wp_schedule_single_event as follows in my functions.php file:

function do_this_one()
{   
    $tokeny = $wpdb->get_var('SELECT oauth_token FROM wp_q33uds_twitteruser WHERE twitter_handle = "manas_oid"' );
    $token_secrety = $wpdb->get_var('SELECT oauth_token_secret FROM wp_q33uds_twitteruser WHERE twitter_handle = "manas_oid"' );
    $connection = new TwitterOAuth(CONSUMER_KEY, CONSUMER_SECRET, $tokeny, $token_secrety);
    $response = $connection->post("statuses/update", array('status' => 'vaudevillains'));
}
date_default_timezone_set('Asia/Calcutta');
$myDate = strtotime($_SESSION['date1']);
$now = time();
$ti_one = $myDate - $now;

add_action( 'my_new','do_this_one' );

$this_time = time() + $ti_one;

wp_schedule_single_event($this_time, 'my_new' );

In another PHP template, I’m storing the contents of the date specified by the user in a form as follows:

    if(isset($_POST['submitted']))
    {
        $_SESSION['date1'] = $_POST['date1'];
    }

However, the event scheduled in my functions.php file doesn’t seem to work. The cron job is never scheduled as intended. I’m not sure how to schedule this event on submission of a form.

I also tried something like this inside the template instead of including the event in my functions.php file:

if(isset($_POST['submitted']))
{
    function do_this_one()
        {   
            $tokeny = $wpdb->get_var('SELECT oauth_token FROM wp_q33uds_twitteruser WHERE twitter_handle = "manas_oid"' );
            $token_secrety = $wpdb->get_var('SELECT oauth_token_secret FROM wp_q33uds_twitteruser WHERE twitter_handle = "manas_oid"' );
            $connection = new TwitterOAuth(CONSUMER_KEY, CONSUMER_SECRET, $tokeny, $token_secrety);
            $response = $connection->post("statuses/update", array('status' => 'vaudevillains'));
        }

        date_default_timezone_set('Asia/Calcutta');
        $myDate = strtotime($_POST['date1']);
        $now = time();
        $ti_one = $myDate - $now;

        add_action( 'my_new','do_this_one' );

        $this_time = time() + $ti_one;

        wp_schedule_single_event($this_time, 'my_new' );
}

The above approach does schedule the my_new event on form submission. However, the do_this_one() function is never called when the scheduled time of the event passes.

What seems to be wrong with both my approaches? And how can I schedule a cron job on form submission?