The secret generally lies in the fact that the smoke from the cigarette or pipe held in the hand is not usually drawn through the mouth. Rather, it usually passes down a hidden pipe in the arm to a bellows in the figure, where it is then transferred back up to the mouth to be expelled. A very ingenious means of creating the illusion of smoking without the complications of creating a tight seal at the mouth.
From the eBay listing:
GENTLEMAN SMOKER AUTOMATON - The man has a papier mache head w/ open mouth, glass eyes, bisque forearms, and holds a black cigarette holder in right arm. When wound, music plays, he raises right arm to mouth, and turns head from side to side. 24" (62cm) Bottom of base to top of hat.
Here is the full eBay listing for Gentleman smoker automaton from 1905