Unix time is not UTC-based. It counts the number of seconds passed since a certain point in time, which may be described as date and time expressed in any time zone you like. It just so happens that in UTC it is easiest to remember for a human what this point was, since you get a lot of zeroes at the end.
Edit: I’m not entirely correct here, as aside from UTC the time zone, there is also UTC the time standard. See below.