Aww that's so sweet!
Genevieve always naturally wanted to go on her back as well, but she needed to be in a blanket and not in my bare hand, until recently. Somehow the blanket made it all totally acceptable.
Now, the first thing she does in the mornings when I take her out of the cage is fall back on my index finger and have my cup her with my left hand. We just very recently worked up to her letting go of my right hand, but she still grasps the fingers in the hand she's laying in. Once in a while she'll totally let go.
It's great that Kyoto trusts you and is confident enough to do that!