Transfer half of avocado mixture to another medium bowl.
Add tomatoes to first medium bowl and cucumber to second bowl. Season salsas to taste with salt and pepper. (Can be prepared 4 hours ahead. Cover salsas separately and refrigerate.)
Rub each steak all over with 2 teaspoons olive oil.
Sprinkle each side of each steak with 1/2 teaspoon ground cumin; rub in to adhere.
Sprinkle steaks with salt and pepper.
Heat 1 tablespoon oil in each of 2 heavy large skillets over high heat.
Add 2 steaks to each skillet; cook until deep brown, about 2 minutes per side. Reduce heat to medium; cook steaks to desired doneness, about 2 minutes longer per side for medium-rare.
Transfer to plates.
Serve with tomato-avocado salsa and cucumber-avocado salsa.