Swear at them! Aphids are extremely sensitive to impolite language. At least. . . that's what I claim when people catch me cussing at them in my garden.
No, if they started dropping off, your neem oil is enough. If not, you can also try spraying with a weak solution of dish soap (and you can buy commercially-prepared insecticidal soap if you don't trust yourself to mix it right). Like many pests, aphids lay eggs that will continue to hatch over time, so re-treat your plant every couple days til you see absolutely no more bugs appearing. And spray any plants near the one where you found the aphids, because they spread fast. It's not death, though. Aphids happen. Keep an eye out and your plants should be fine.
And. . . welcome to the forum!