My personal theory, which is a lot of fun to think about if you ever go back and rewatch the shows, is that The First and Jasmine were rivals, and they're both basically racing to prevent the other from winning. Dueling Apocalypses, if you will. Sunnydale is unaffected by Jasmine because the First is somehow keeping her out.
And in "Angel," when Connor sees the vision of Darla, that's not actually Darla. What is the First's one known power? To take the form of dead people. I think the First knew what Jasmine was up to, so it took the form of Darla in order to prevent Connor from releasing her into the world.