Hear me out.
I have seen people theorizing that Rio is angry at Billy/Wiccan bc he broke the rules of death, possessing a body that wasn't his and therefore causing problem to her
And we have seen Rio saying to Agatha "That boy isn't yours", what if she is trying to prevent the same to happen? Rebembering Agatha because she is going to take his soul like she did with Nicholas, she doesn't want she to be hurt and mad at Rio again by that "that child isn't yours, so dont blame me for what I have to do."
I think it makes more sense to why she seemed worried about saying that before Agatha kissed her, she cant endure being loved again if she have to betray Agatha again