We don’t use timezones in Postcrossing normally, because that way lies madness… but in the first year of World Postcard Day, sooooo many people were confused with the concept of “October 1st in UTC time”, that we decided to make a little exception and expand the time for the badge to also include local timezones. So that means if you draw an address during October 1st either in UTC time or in your own timezone, it’ll count towards the badge.
That said, we would really prefer if people stick to their own timezones and don’t try to knock the server’s socks off by requesting hundreds of addresses at UTC midnight, when we’re supposed to be going to bed… 
So, although you can request addresses in the hours between UTC midnight and your own midnight (and they’ll count for the badge), we would recommend everyone requests addresses on October 1st on their own timezone — it simplifies things, and makes it easier for us to have a good night of sleep. 
I hope that helps to clarify!