Story boost just makes some quests "done", without, well, doing them. Just look around for blue quest markers and do those. Also, clearly, you need to be level50 for them, but I guess that's done and over with.

PS: Mimilu wrote about Titan/Ifrit/Garuda...That's what she meant by ARR primals, so she said that you need to unlock them through your Grand Company. That's a good place to go and start looking out for those markers.