If this is a connection (i.e. the next flight takes off less than 24 hours after arrival into SFO) and the next flight isn't a separate trip in the itinerary, then IATA most significant carrier rules apply which state that the baggage rule of the first carrier which crosses an IATA zone (i.e. Asia to the Americas) applies to the entire itinerary.
If the carrier chooses not to follow the rules, that must be explicitly stated on the ticket though. It is assumed MSC applies unless and until the carrier explicitly tells you otherwise.
Baggage allowance can be... complicated. There's a lot of moving parts. Part of it comes down to the most significant carrier rule as I stated earlier for international itineraries. Another consideration is what flight number is tied to what segment. For instance if the Alaska flight has a Qantas flight number applied, Qantas baggage rules apply and I think on all Qantas flights at least one bag is allowed (even on the cheapest red e-deal). Then of course the fare class you are booked into makes a difference too. For instance, if this is booked as a classic award on Qantas, what does that correspond to for baggage allowance? On some frequent flyer programs that corresponds to a regular economy fare that gives you a free bag, on others not so much. That's one of the reasons why I have FF status since I'm always guaranteed to have at least one free bag.
