Factions can be controlled fairly predictably; it's just that not everyone has learned how yet.
Basically, you need to check the faction page once a warning comes up and evaluate the situation. What I do is fix the opinion of low opinion faction members where it makes the most sense to do so. This is really no different from the old system. Keep in mind the various tools are: send gift, honorary title, fix whatever ailes them (e.g, "wants control of ..."), send chancellor to improve relations, educate child, give a counsel seat, etc.
But now you have more tools. You can send your spymaster to scheme in one of the faction member's location. But you can also get more creative. I've begun to plot assassinations against key rivals to either weaken the heir (I use gavelkind, so if they have more than one heir, their holdings split) or pass it off to an heir that is likely to have a higher opinion of you. I have also been imprisoning and revoking titles. This is like a preemptive action. If they rebel then you can take them down one by one rather than as a group. Just be careful not to do it in a way that reduces general opinion.
Overall, the new faction system is a major improvement over the old rebellion system. There was just a boring and lame predictability to the old system, where distant rulers would always want to rebel and would frequently do so alone--unless you are a new ruler, then everyone rebelled at once and virtually immediately.
