Look at this pic:
You must be registered for see images
You must be registered for see images
Amaterasu doesn't appear instantaneously. It travels. Look it carefully and you will see blood even already touching the floor, so even before Amaterasu is released, Sasuke needed his eye to bleed a lot, and even when it's released, it doesn't touch Raikage at the start, it converges to hit the target(Raikage), then Raikage avoid it, and then again it continues to travel to hit the Samurai who was behind. So even when Amaterasu is released, it is not that instant. It's only that it travels very fast