If you cut a living tree, or a fairly recently deceased tree, one that is still really "dripping" wet, it is my experience that the very light center areas will indeed darken as they dry. If the tree has been felled for some time, or was dead and well dried before being cut, then you are probably seeing areas of the sap wood and it will not darken appreciably. I cut into a stump that someone gave me not so long ago, a huge thing that I thought would be dry, and it literally slung water from the chain saw blade as I cut it. The center areas of that stump were so light in color as it was cut that I would have doubted it was walnut had I not seen the tree beforehand. It darkened in a 24 hour period as the surface water left it.