Unlike the civil calendar in which one day becomes the next at the stroke of midnight, the transition from one day to the next in the Jewish calendar occurs somewhere between sunset and nightfall. Therefore the Jewish date will always overlap with two days in the civil calendar, and the same is true of the reverse.
The reason a competent Jewish Rabbi asks for the city where the event took place is to determine when nightfall occurred on the date you selected (which depends, of course, on where it occurred). Once a competent Jewish Rabbi does this he can determine whether your event took place in the first or second of the two Jewish dates corresponding to the civil date.
