How to deal with timezones between server and client?

Your problem doesn't involve timezones at all, just the fact that clients can turn their clocks or have their clock skewed considerably. For that the fix is to poll the server every once in a while for an offset fix to use in calculations.

In fact, you don't even need date objects. There is a certain universal instant in time when the auction ends. Let's say it is 1375960662823. Right now, the universal instant in time is 1375960669199, so from that we see that the auction ends in 6 seconds (1375960662823 - 1375960669199 ~ 6000 ). It will end in 6 seconds regardless if I am in Morocco or Japan. Do you understand it yet?

To generate these numbers, on the client side you can call var now = Date.now() + skewFix where skewFix is the correction that needs to applied in case client has time skew or manually set their computer to wrong time.

In PHP, you can generate it with $now = time() * 1000;

This is rather a typical subject yet very complex for most to understand. First thing, you never mention the DAYLIGHT SAVING. yeah I am increasing your tension :).

Now let us see how we can do this. You did a good job by saving the Time in UTC. Now, I hope you have registered members and that each member has ability to set their preferred timezone, otherwise you will show Server' timezone based time to them.

When you through "start time" to user you must send them after converting UTC time to their time, similarly when you accept TIME from browser be it user action or javascript you need to convert that time to UTC considering the fact that user is that time zone that he select for his profile.

Hope that clear the idea on where you are going wrong? Please read through day light saving as that will play an important role too when you move ahead with other logic on same.

EDIT:

You can use javascript's Timezone offset, for auto submission and user input based on his settings.

Date in JavaScript uses local timezone. You should get UTC time for the user and send it to the server

new DateThu Aug 08 2013 17:00:14 GMT+0530 (India Standard Time)(new Date("Thu Aug 08 2013 17:00:14")).toUTCString();"Thu, 08 Aug 2013 11:30:14 GMT"

This will resolve the timezone issue between the server and client.