In a medium saucepan over medium-high heat, warm the olive oil. Add the onion and garlic and cook, stirring occasionally, until soft, about 5 minutes. Add the remaining sauce ingredients. Bring the mixture to a boil, then reduce the heat to a simmer and cook, stirring occasionally, until reduced to ½ cup, about 10 minutes. Purée the sauce in a food processor or blender. Allow to cool; cover and refrigerate until ready to use. Bring to room temperature before serving.
In a small bowl mix the rub ingredients. Press the mixture into the surface of the tri-tip, cover with plastic wrap, and refrigerate for 3 hours or as long as 24 hours. Allow the tri-tip to stand at room temperature for 15 to 30 minutes before grilling.
Soak the wood chips in water for at least 30 minutes.
Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Drain and scatter the wood chips over lit charcoal or put them in the smoker box of a gas grill, following manufacturer’s instructions. Sear the tri-tip over direct medium heat, with the lid closed as much as possible, turning once, until both sides are seared, about 5 minutes total. Then continue grilling the tri-tip over indirect medium heat, with the lid closed, until cooked to your desired doneness, 20 to 30 minutes for medium rare. Remove from the grill and let rest for 3 to 5 minutes. Cut the roast against the grain into thin slices.
Build each sandwich with slices of meat and a dollop of sauce. Serve warm or at room temperature.