The timezones thing, of course, is just a way to have the younger twin be born "a year ahead" of the older twin by having their births be in two different timezones. Only practical way that would happen would be aboard a ship, because 1) babies born aboard an airplane would probably end up using the time zone of departure or of destination for their birth, and so twins would not be counted as being born in different time zones. And 2) any land-based transportation such as a car or a train would likely pull over (or in the case of a train, let the pregnant woman off at the nearest station) so that the woman giving birth doesn't have to do so in a moving vehicle. So a ship is the only moving vehicle where this kind of thing could likely happen, as there's no option of getting off in the middle of the ocean. It could happen while crossing time zones east-to-west, but crossing the International Date Line west-to-east makes more of an interesting thought experiment.
Yes, I've given this silly joke scenario way more thought than it really deserves. :-)
Doesn't even have to be the International Date line, any two timezones work.
The riddle explanation was something like: A baby is born in New York City at 12:15 AM on January 1. Thirty minutes later, another baby is born in Los Angeles, where the local time is 9:45 PM on December 31. Although the New York baby is actually older by 30 minutes, the calendar dates make it appear as though the Los Angeles baby was born first.