Not only will the clock on your iPhone automatically turn back to 1 AM when 2 AM is reached, but it could also shrink back an additional hour after you go to sleep. This just happened to my iPhone. The iPhone had correctly displayed 1 AM when the moment came to turn back the clocks one hour, but after I woke up in the morning, it somehow lost an additional hour all by itself during the night.
The actual time in NY was 10:15 AM when I got up, but the iPhone was displaying 9:15 AM. I came here to look for others reporting a similar anomaly, but finding none, I simply turned off the phone for a couple of minutes, and I turned it back on. That cured the glitch. The iPhone is now is sync with the correct local time.