I don't think that it has to do anything with time. Football is very popular in both Japan and South Korea, and this has been the case for the past decades. I am not exactly sure why the Asian teams underperform at international level. Despite their huge population, China and India almost never qualifies for the World Cup. Asian players are in general shorter compared to the Europeans, and that maybe the reason. But in that case Brazil and Argentina should not perform so well. I strongly suspect that there is some other reason.
The reason is that the Chinese and Indian Championships are very weak compared to the European Championships. Although the Japanese J1 league looks more interesting, the Japanese team also shows very weak results in the World Cup playoffs. Anthropometry also plays some role, but the main role is played by the competitiveness of the championships.