PHP & MySQL: Converting Stored TIMESTAMP into User's Local Timezone

So I have a site with a comments feature where the timestamp of the comment is stored in a MySQL database. From what I understand, the timestamp is converted to UTC when stored, then converted back to the default timezone when retrieved. In my case, my server is in the Central Daylight Time timezone (CDT).

I have a plan to get the timezone from each user via entry form. I just wanted to know how to convert the TIMESTAMP value into the user's timezone.

• First, would I convert from UTC to local timezone? Or CDT to local timezone?
• Secondly, how would I go about doing that in PHP? Would I just do:

$userTimezone = new DateTimeZone($userSubmittedTimezoneString);
$myDateTime = new DateTime($storedTimestamp, $userTimezone);

...or is that not correct?