I don't think your question invalidates the fact that a majority those groups did support Prop 187 as a solution to a percieved problem. Hypothetically, if the Pubs had supported it better, post election, they may have picked up more permanent support from these groups.
But to answer your question, I think that, on other issues, the Rats offer more to these groups, which tend to be of lower income, than the Pubs *did*. (Notice the use of the past tense there.)