Just as Oded has answered. You need to have this sort of detection functionality in javascript.
I've struggled with this myself and realized that the offset is not enough. It does not give you any information about daylight saving for example. I ended up writing some code to map to zoneinfo database keys.
By checking several dates around a year you can more accurately determine a timezone.
Try the script here: http://jsfiddle.net/pellepim/CsNcf/
Simply change your system timezone and click run to test it. If you are running chrome you need to do each test in a new tab though (and safar needs to be restarted to pick up timezone changes).
If you want more details of the code check out: https://bitbucket.org/pellepim/jstimezonedetect/
