Here are two explanations.
The first possibility, and most likely (in my opinion), is that this is a convenient theatrical construct to convey the creepiest or most dangerous time of the day – where it’s dark, cold, and things go bump in the night. There is always plenty of time for those who wander in the darkness to do their bidding. This is unlike just before dawn where one can be optimistic of coming light. And yes, I agree that with the coming of dawn, the period of risk is over until the approach of the next midnight.
The second possibility is to apply a little science. Assuming a day is exactly 24 hours, midnight is when you are 180 degrees longitude away from noon on the other side of Earth. Where it’s “high noon”, the sun is at zenith – the highest point in the sky. And this “line” of high noon moves around the Earth as it rotates on its axis. So, a gremlin would somehow have to know that it is “at opposite” to noon. That is the only non-fantastical answer. It also answers the question of whether you cross time zones. It doesn’t matter what time zone you are in and whether you are crossing time zones.