Nuts or other additions are added just before the fudge begins to cool and firm up, or "set." Tom told us that fudge actually sets faster on a warm table than a cool one. This apparently illogical observation spurred much discussion, a little research, and a tentative conclusion (see The Marble Slab Paradox.)
The final stage of the paddling is an artful arrangement of the fudge into a long loaf, ready for slicing.
Then Tom begins to "paddle" (stir) the fudge, initiating the formation of the tiny microcrystals that ultimately will cause the fudge to solidify.