Mio was the original sacrifice, and Miyako was the next head and more powerful one (Although Natsuki had noticed that Mio was more powerful). The relationship between the sisters was also strained.
When Natsuki heard about Mio being sacrificed because she was inferior, elder Unkai complained a lot about him, but when Natsuki mentioned "Shouldn't you guys prepare the best option as an offering? If I were to require something, I would prefer the best option, not the remainders"... Elder Unkai thought about it, and agreed with Natsuki (to his surprise).
And so they changed Miyako to be the sacrifice, and that caused a crisis on the prideful young girl, but the decision had been made. Miyako now understood everything that her older sister went through, but Mio (who was pretty angry and Natsuki for the change), told Miyako that she would handle everything.
Thus the arrogant Miyako felt despair, was comforted by her "inferior" older sister, and became a super siscon.
Natsuki felt a little bad for her, since his words essentially became a death sentence to his classmate, but he didn't really care about her that much.
And Elder Unkai was actually more reasonable than he imagined, just pour in some logic, and everything went smoothly with her.