See https://discussions.apple.com/thread/7294687 for full discussion.
Don’t touch that dial!
I lay awake last night thinking about the iPhone weather app having the wrong time for the Central Time Zone.
It occurred to me that the time given is Greenwich Mean Time. I even got up and looked up the time in London. It was one hour later than Greenwich Mean Time because Britain is daylight savings time. The British time was one hour later than the time in weather app.
This morning I checked my wife’s iPhone. It had the wrong weather time, and she is still on iOS 9.0.1. I asked several people in a fitness center and they reported that their iPhone weather apps had the wrong time. Some even reported that this started at the end of last week.
I think what has happened is that whoever maintains the data for Apple’s weather app took off the -5 adjustment for Central Daylight Time. So, the problem is not in your phone and no kind of reset will fix the problem. We’ll just have to wait for somebody in Apple to put the correct adjustment on Central Daylight Time.
Now I have to find Apple’s Feedback page and post the above to it.