Definitely what you just said there ^
I won mine today (last night?) at 1:01 AM... I was the first to win today. Others have won at XX:36, :34, etc. Just because someone won at a certain time doesn't matter because it might not be that time every time. Furthermore, your clocks will be different. My PC clock right now is different than my phone's, and both are probably different than the game server.
That is all besides the point though. Even if you did manage to pinpoint the time for the next prize, there are still other people entering, probably at the same exact time as you. Ok, 4AM will have less entries, and 5AM even less than that, so your odds are different... that is really as precise as you can get it.
Worst of all? Even that doesn't matter, because as far as any of us know the time is completely random. You will never figure out what time the next one will be awarded. If any of you do, feel free to post the news about your 30 free 360s that are coming. That said, it is kind of foolish to assume that because someone else won at 02:37:59, you are more likely to win if you enter at the same time. It is random, what if they decided that for that 15 minute block it will be at 02:43:13? It would be like playing the winning lotto numbers from the week before because hey, since they came in once they might be more likely to come in again! The closest you can narrow it down is to the 15 minute blocks, maybe with better odds during the night.