Where I live, the Hispanic leaders and business groups have endorsed Republican candidates in all political races except perhaps a few local ones. Generally, if exit polling were done on "3rd generation and back Hispanics" versus "2nd generation and newer Hispanics", you'd see a world of difference. (They're not really even the same group, culturally, IMO). That's the point of the article.
Voting GOP is not necessarily voting against illegal immigration, though. I am sure that there are candidates out their who would be willing to stop illegal immigration if a majority would support doing so. But for some reason, those guys never get elected.