I disagree.
As recently as 1996, Asian American voters gave Bob Dole a plurality of 48%-44% over Bill Clinton.
What's happened is massive legal immigration from Asia.
Asian Indians have been the largest immigrant group from Asia for about 20 years, and they voted 90% or higher for Obama in 2004 and 2008.
I believe Chinese are the second largest Asian group in recent decades, and they vote around 75% for the Democrat Party.
The changing character of Asian immigrants also plays a role.
Asian Indians are often very well educated, but they remain overwhelmingly Leftist, like their home country.
Immigrants from the other Asian countries usually have limited education and limited skills, which makes them a prime voting target for the Democrat Party.
Which brings us to the biggest Communist country of them all: the People's Republic of China.
There are a lot of Chinese-Americans in the United States. Many of them constitute immigrants who suffered tremendously under communism, through the Great Leap Forward and then the Cultural Revolution.
Yet Chinese-Americans are also a highly, highly Democratic constituency. One exit poll put 73% of Chinese-Americans as voting Democratic. Why does the Schwarzenegger experience not resonate with Chinese immigrants?
One reason might be that most Chinese immigrants are not communist refugees. Many anti-communist immigrants were persecuted as a specific class or individually by communist governments. They then fled to the United States. On the other hand, a lot of Chinese immigrants came to the United States as students, workers, or via family connections. Many of them represent people who benefited from the system in China. This is especially true for those who came as students or workers.
There is also the fact that China's Communist Party is by far the most successful of all the communist parties out there. This dilutes the potential opposition against it. For instance, the Chinese community would probably not support an American embargo on China aimed at toppling the communist government there. This is quite different from the Cuban emigrant community.