@Mujahid If the printed time and the saved time are the same it probably means your server is not in the same timezone as you. With that said, you have to manually set the default timezone for your PHP script at the top of the file, or get the DateTime by defining your timezone explicitly. Here's the code:
$dateTime = new DateTime("now", new DateTimeZone('America/Los_Angeles'));
$add_date = $dateTime->format("Y-m-d H:i:s");
echo $add_date;
Here's a list of time zones that PHP supports, just find yours and replace America/Los_Angeles with it.
http://php.net/manual/en/timezones.php
Here's a good tutorial on PHP DateTime and DateTimeZone...
http://ditio.net/2008/06/03/php-datetime-and-datetimezone-tutorial/
Hope this helps. Good luck.