I gatherMy understanding is that the question is not regarding why Columbus believed he had reached Asia at large, but why he mistook San Salvador for Japan. If so, the answer (lacking the relevant primary source material) appears to be as follows:
The Bahamas, which he believed were Japan, are north of Cuba, which he believed was China. (according to the question's source) At that time, the West was familiar mainly with the southern portion of China, which was more accessible to Europe by land via India and Indo-China, or by navigation along the southern coastlines. If so, Columbus, as well as most Europeans familiar somewhat with the Orient, would have understood that Japan was north of China, since Japan is indeed north of the southern coastal regions of China, those regions which the West at that time typically identified as China.
Map of Eastern China and Japan, published in 1570. Note the region label China, and the illustration of ships coming from the south in the East China Sea, towards Japan in the north and China to the south and west. In light of this map, Columbus's opinion regarding the Bahamas and Cuba is quite understandable.
We might also add that the Bahamas are a chain of islands, similar in that respect to what was presumably known regarding Japan, whereas in comparison, Cuba appears to be a large landmass, similar to what was known about China.
Contemporary Map of the West Indies, showing prominently Cuba and the Bahamas.
If so, it would be logical to conclude that if he were indeed in Asia, the more northern island he discovered, an island in the Bahamas, was Japan, and the land to the south, Cuba, was China.
If he immediately believed he was in Japan upon landing, it would have been because his charts indicated he was heading towards the more northerly regions of his intended Asian target, i.e. Japan. If he only concluded the Bahamas was Japan after reaching Cuba, it would have been apparent that Cuba was south of the Bahamas, and so the the Bahamas were Japan and Cuba was China.
If this is not the question, then my answer is superfluous, and LateralFractal's answer is excellent.
