From what I've read, Asians used to vote Republican during the 1970s and 80s. The gap narrowed dramatically under Bill Clinton during the 1990s. From 2000 on, a clear majority of Asians have been in the Democratic camp.
It was largely anti-Communism. Most ethnic Chinese and Filipinos and almost all ethnic Koreans and Vietnamese voted with the most strident anti-Communist party of the time because they had fled Communism or dreaded Communism in their homelands. Japanese and South Asians whose ancestral homelands had comparatively little experience with Communism didn't so vote. (The Japanese voted much like Jews). After about 1980 the PRC did an effective PR job in ethnic-Chinese communities as the PRC dropped any semblance of an effort to spread its "revolution" abroad and became a big trading partner. Vietnam has done much the same, and the Commie threat in the Philippines petered out after the People Power revolution.
The only expansionist manifestation of Communism in Asia is now North Korea, and Koreans seem to be more Republican than other Asian groups.
Koreans are definitely solidly Democratic (indeed, despite being the only large Asian group with an evangelical Christian "tradition"). The Vietnamese are still Republicans, though. I think Filipinos might be Republican, too; certainly the Philippines was one of the only countries worldwide where Bush was still viewed positively by the end of his Presidency. There is of course also a Christian tradition in the Philippines, although they're mostly Catholic (although that Iglesia ni Cristo thing resembles some of the weirder branches of evangelical Protestantism). There's also a lot of anti-Muslim sentiment in most of the Philippines.
All the evangelical Christian Koreans I know are economically liberal, but definitely social conservatives. Some are solid Democrats but it can be easy to use social issues to sway their votes to the Republicans.
