I don't think it works the same way as it used to so I think it depends what OS you are on and when you last set the clock you want. If it's a widget that's been there for years it's probably what the problem is. I'm not sure when the system changed.
In earlier times, you'd select 'edit widgets' and you would drag a clock widget to the right, click on it it would turn over and then you would tell it what place you wanted it to show the time for.
If you have one which you did like that on a previous OS, in my experience the clock face won't get the day and night right, and if you try to add another one like that you won't be able to make it flip around to change the city.
Every one you drag from default on the left just shows the current time and can't be changed now.
What you have to do now is when you have selected 'edit widget's, look over to the far left settings and find 'clock'
If you go into 'clock', there you will find various options for the clock and you will see there are specific ones which show the current time and specific ones which show time in other cities.
You have to drag one of the models for other cities to the right, then flip it and tell it which city you want.
Then it should get it right in my experience
It seems to be how it works for me.
