Medi-cal and the Washington state medicaid programs both allow for non-citizens. However, they do not use federal funds to cover non-citizens, they use state funds. They leverage their higher tax revenues to cover.

Federal medicaid funds do not go to illegal immigrants. If a state wants to cover them they have to do that out of state revenue.

Since medicaid is partially state funded and mainly federally funded that's what opens up the door for states to have different rules for eligibility (expanding beyond the federal standard). However, the states have to cover the excess when they decide to do that.