It looks to me like the materials dry out and take their designed shape. If you watch the videos very carefully you can see them look wet in the beginning and drier as time passes. Well, I see it at least. I could be wrong.
For the "programmable" wood, yes. This isn't necessarily the case for the other materials. It appears they mean programmable in the sense of shape memory alloys of a few years back. Given a set of conditions, the material assumes a predetermined shape based on the architecture of the material.
It is not what many of us think when we imagine "programmable materials." When there is a computational substrate driven by software that can assume shapes based on the software instructions... that will be programmable materials.
