You are right about the divider, but the 'liquid' is actually the tea which has a special gelatine added to it. Once the tea gelatine is set, it is blitzed up very fine, but because this gelatine isn't starch based and the blitz is fine, you don't perceive it as a liquid (unless, perhaps, you knew what was going on in advance). However, since it is not a liquid, the heat transfer between the hot and cold elements is slowed significantly as is the rate of mixing (which is what would happen normally if it were actually two liquids).
You'd still need to serve and drink it quickly anyway and without agitation, as even though it's heat transfer between two solids (or sets of solids), since they are in direct contact it will eventually come to the same temperature.
Great report.

I would like to try The Fat Duck one day; hopefully it will still be around (even if in Australia) when I'm ready.