One could also argue that the rate of cultural change by immigrants is lessened by the need for those immigrants to operate within the system, and by their relative lack of influence on the culture as a whole.

You're probably going to have a hard time finding a job in Japan that isn't "English Teacher" if you can't speak Japanese effectively - which is an example of the parent culture exacting a price in the form of partial assimilation for the opportunity of cultural exchange.

Plus, most immigrants to Japan are probably going to be from China, Korea or other Asian countries, simply because of proximity. Immigration doesn't necessarily have to mean millions of Westerners.