Prepare the grill for direct cooking over high heat (about 450° to 550°F). Bring a large pot of salted water to a boil on the stove for the pasta.
In a small bowl combine the rub ingredients. Lightly brush the tuna steaks on both sides with oil and season evenly with the rub.
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Brush the cooking grates clean. Grill the tuna over direct high heat, with the lid open, until cooked to rare doneness, 2 to 3 minutes, turning once. Remove from the grill, let rest at least 10 minutes, and then cut into bite-sized pieces. Meanwhile, cook the pasta according to package directions. Drain the pasta, reserving about ½ cup of the pasta water.
Brush the cooking grates clean. Grill the tuna over high heat, with the lid open, until cooked to rare doneness, 2 to 3 minutes, turning once. Remove from the grill, let rest at least 10 minutes, and then cut into bite-sized pieces. Meanwhile, cook the pasta according to package directions. Drain the pasta, reserving about ½ cup of the pasta water.
In a large skillet over medium heat on the stove, warm 1 tablespoon oil, add the onion and thyme, and cook until tender, about 7 minutes, stirring occasionally. Add the garlic and lemon zest and cook for 1 minute. Add the wine, bring to a simmer over medium-high heat, and cook until the skillet is almost dry, 3 to 4 minutes. Add the cream and return to a simmer. Cook until the cream has thickened, about 5 minutes. Remove from the heat, stir in the lemon juice, ¾ teaspoon salt, and ¼ teaspoon pepper, and then fold in the tuna and 2 tablespoons of the chives. Keep warm.
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Combine the pasta with the sauce and stir to coat, adding a few tablespoons of pasta water as needed to help the sauce coat everything. Season with salt. Serve right away in shallow bowls, sprinkled with the remaining 1 tablespoon chives.