Thick layer of egg formed at the bottom of sponge cake
From the video, it looks like medium eggs (about 50g) were used. If like me you usually buy large eggs then the extra yolk could be as much as 50g. So I'd suggest cutting back on the yolks slightly. The water bath should help cook the base. Also definitely use a metal tin, as in the video: glass or ceramic containers do not conduct the oven's heat to the bottom of the cake so efficiently.

Finally you mention whisking: definitely whisk to stiff peaks for the egg whites. But for the batter, you don't want so much air. Instead the aim is to make a stable emulsion.