4 Cover the grill and cook until the temperature of the interior of the tri-tip reaches 120°F for a rare roast, 130°F for medium-rare and 140°F for medium. At this point the meat will take anywhere from 20 to 40 minutes to cook, depending on how hot your grill is, how well done you want it, and the size of the cut.ri-tip roasts range from 2 1/2 pounds to 4 pounds. Figure on 1/2 pound of meat (before cooking) per person. A Santa Maria rub has salt, pepper, and either garlic salt or garlic powder. That's the base of the rub, anything beyond that is optional.