Do unix timestamps change across timezones?

Unix timestamps do not change accross timezones, they are created for the purpose of having a standard time across globe.

NOTE:- Timestamps are calculated on the basis of current time in the computer thus do not rely on them until and unless you are very sure about the time settings in the participating machines.

The definition of UNIX timestamp is time zone independent. The UNIX timestamp is the number of seconds (or milliseconds) elapsed since an absolute point in time, midnight of Jan 1 1970 in UTC time. (UTC is Greenwich Mean Time without Daylight Savings time adjustments.) Regardless of your time zone, the UNIX timestamp represents a moment that is the same everywhere. Of course you can convert back and forth to a local time zone representation (time 1397484936 is such-and-such local time in New York, or some other local time in Djakarta) if you want.

The article at http://en.wikipedia.org/wiki/Unix_time is pretty impressive if you'd like a longer read.

Unix time is defined as the number of seconds that have elapsed since 00:00:00 Coordinated Universal Time (UTC), Thursday, 1 January 1970. So the answer is no