Think of it in terms of two buckets - a warm bucket and a hot one - most of the heat is lost at the top of the bucket. In the warm bucket there's a warm trapped layer in the middle of the bucket - it's trapped by falling cold water. In the hot bucket the middle layer is more energetic, and breaks through to the top of the bucket where it cools quicker. The hot bucket even pushes down cold water with more force. The distribution of heat in the two buckets is completely different.What puzzles me is: the temperature of the 'hot water' will drop. On the way, it will pass the temperature that the 'cold water' started at. Unless there is some other factor that the experimenters haven't told us about, it is then the same stuff at the same temperature that the cold water was (it is now 'cold water') but later. How can it then (from that temperature) cool faster and overtake than the other lot of water?
IF.......You had an stirrer going in both buckets......the cooler bucket would freeze first.
I heard about this competition a while back. I think they were looking for a fancy pants demonstration. Doing it with thermal cameras and a walk in freezer might be a thing - then quite a bit of experimentation to get the optimal temperatures for the demonstration. It will probably be done by some precious rich kid nerd (with lots of help) who will then go on TED Talks, and make us all want to vomit.