Asian Americans voted that way as a whole, according to exit polls.
Yes, but much if not most of that was due to demographic changes within the Asian-American community, and the population of registered voters therewithin. Proportionally fewer Koreans, Chinese, South Vietnamese, and other demographics who typically vote(d) Republican for socioeconomic reasons and/or because of anti-Communism; proportionally more Cambodians, Filipinos, Bangladeshis, Indians, and other demographics who typically vote(d) Democratic for socioeconomic reasons and/or because their backgrounds didn't have the sociopolitical baggage which prompted other Asian groups to vote Republican; and a large number of these "new Asians" had turned 18, been naturalized, or became eligible to vote sometime during Bill Clinton's second term.
That said, the rise of the Evangelical Protestant contingent within the GOP so far mentioned by others in this thread, or some other aspects ("Southern-ization," "prolitar-ization," etc.) of the still-ongoing Nixonian realignment of the party overall, probably does account for at least some of the change in the Asian-American vote remaining after accounting for demographic change.
