This is a good question, and a valid concern. I've discussed this with other mods, and I think in this case, it is clear that Persona 4 Arena is a different genre and a possible gateway for fans into the series who might not have played the previous game. While it is a sequel of sorts, I don't think it would be fair to have unmarked spoilers for no reason either.
So the policy on this would be that spoilers for previous games should be marked clearly if someone wants to discuss plot points, but at the same time, we should realize that not everyone is malicious with this. So if something that's unmarked, it would be good to:
a) not quote that unmarked spoiler
b) advise the person to mark the spoiler before someone who might not want to see it, sees it.
If you want to share this with people posting in the P4A threads, that would be good too.
As for other multi-game franchises, I don't think it directly applies to every franchise. Some games expect that someone who is playing the current game knows about all the major events in the previous games - either through a summary in the game, or from having played those games themselves. An example would be Mass Effect. Hence in a Mass Effect 3 thread, unmarked spoilers for Mass Effect and Mass Effect 2 wouldn't be in bad faith, because it is hard to argue that someone playing Mass Effect 3 is trying to avoid spoilers for the first two games.