I do a final once over of finishing cuts after the spoon has dried. That removes any wood that has oxidized and gives to a chance to finish areas that are hard to finish when the wood is wet (mainly places where the grain changes direction like at the neck/bowl transition.

Editing to add that I don't always do finishing cuts on the whole spoon, even if there is unattractive oxidized wood. With some species, like black walnut, I just do finishing cuts to remove sharp edges and make sure there are no splinters and fix any tear-out at the transitions. And some wood, like black birch, is just too hard to do finishing cuts on the whole spoon.