I think that would be the expectation of most non-engineers, assuming they set the new time zone before arriving and if they even considered edge cases like that. It's also how most alarms work, whether mechanical or digital.

I think that's pretty hard to do in these post-concord days?

Though if you lived close to a time zone border it could be a problem. There are towns straddling the Queensland-New South Wales border in Australia. There is a one hour time difference between the states for half of the year (NSW does daylight saving, QLD does not). I've always wondered how local businesses deal with that.