DateTime timezones

I am writing writing some code which records when a user (user x)
performs an action. I need to be able to tell other users when 'user
x' performed said action, but relative to the end user's timezone.

My users can all be in different time zones. What is the best way to
store a timestamp for an action and then to display a human readable
time of the action in someone's time zone?

For instance, 'user x' uploads a file at 13:00 UTC. This needs to be
presented as 21:00 for 'user y' in Adelaide.

Currently, my script records the unix timestamp as a marker of when
the action was performed.

I had hoped that the code below would work, but it doesn't appear to:

$actionTime = 1215602000;
$dtz = new DateTimeZone('Australia/Adelaide');
$dt = new DateTime("@$actionTime", $dtz);
echo $dt->format('r');


Thanks!

Martin Sweeney