Two chapters ago, we already saw Hina's price (umbra) was hunger, so I assume she wanted to eat him up...
The umbra is both related to their lux and abstract enough it can mean various things (in most cases). Kairi's umbra is contact, as we know, and as such any contact with others counts but it can be assumed the efficiency increases depending on the intimacy (as seen by him saying 'holding hands will take forever'). As such, we can deduce that Hina's umbra is also more efficient if she eats (Sates her 'hunger' with) the things she desires/wants, in this case Kairi/Ibuki.