The problem is that you're displaying time(), which is a UNIX timestamp based on GMT/UTC. That’s why it doesn’t change. date() on the other hand, formats the time based on that timestamp.
A timestamp is the number of seconds since the Unix Epoch (January 1 1970 00:00:00 GMT).
echo date('Y-m-d H:i:s T', time()) . "<br>\n";
date_default_timezone_set('UTC');
echo date('Y-m-d H:i:s T', time()) . "<br>\n";