@Toon
Most likely it's set by your DS clock, not your opponents. I'm not sure you DS even detects what time the other persons DS is on when it links up with them for Wi-Fi or not, and even if it did it's more likely to be decided by your DS' time than theirs (Just think about Time Zones, it wouldn't be really fair to people in like Australia to constantly have their Shaymin-S reverting because of their location). I however do not have absolute proof of this.
thanks