Previously, Eve had informed Rio that whoever he osculates first would receive the crown.
However, he soon realized that this was not entirely true. As he received the black-stage monarch beast's crown, he discovered that he had more control over it and could give it to whomever he chose.
Rio believed that Eve was the most suitable candidate for the power and responsibility that came with the black-stage monarch beast's crown. He knew in his heart that she was the one he wanted to bestow it upon, and so he did.
He didn't want to burden Lia or his other girls with this task, fully aware that Eve was the right candidate for such responsibility.
When he obtained the crown, he realized that he could control it better and give it to whoever he wanted, which was different from what Eve had previously told him.