Yacon replants can be tricky to store. They will rot if too wet, and will be killed by frost. Best kept cool but dryish, but some people get away with leaving them in the ground all winter. I store mine in almost dry spent compost in a box in a frost-free unheated shed.
On the other hand, oca tubers will survive all sorts of mistreatment, - even being left all winter in a centrally heated room.