***** NOT A TEACHER *****
Please do not laugh, Albert, but the rule seems to be this: IF you are referring to a small island, use "on": IF you are referring to a big island, use "in."
Of course, you are asking: Who decides whether it is "small" or "big"?
The answer seems to be: the editors of newspapers, books, etc.
1. "The airplane crashed into the ocean. The two survivors were able to swim to an island that was less than half a mile in length and width. They stayed on that island until they were rescued." (That is my sentence.)
2. If my memory serves me right, newspapers used to refer to events on Taiwan. Now they all refer to events in Taiwan. (Taiwan surely counts as a "big" island.)
3. I think it is accurate to say that if you are referring to a nation that consists of an island (Taiwan, Iceland, Jamaica, etc.), you should refer to events "in that island."
James