They don't; this article is pure BS, meant to keep the issue alive and scare the GOPers in the border states.
I don't believe that the article is saying that illegals are going to vote to punish Bush (although some illegals do vote), but rather it is saying that relatively recent immigrants who are now citizens and sympathize with the illegals will vote to punish Bush. That would generally include former illegal immigrants who have been amnestied and now have citizenship status as well as legal immigrants generally from the same countries as the illegals. For example, those represented by groups such as La Raza (and there are many more).