Marinate the tuna: combine all marinade ingredients in a medium bowl and mix well. Dice the tuna and toss in the marinade. Cover with plastic wrap and refrigerate.
Make the rice: Bring 2 cups of water to a boil in a small saucepan. Stir in 1 cup of uncooked sushi rice. Reduce heat to low and cover. Cook for 15-20 minutes, until water is absorbed.
Make the avocado mash: combine the avocado, juice of 1 lime and a dash of sea salt in a small bowl. Mash with a fork.
Assemble the sushi tower: Arrange a thin layer of diced cucumbers onto the bottom of a 1 cup measuring cup. Pat down. Place a layer of diced mango on top of the cucumbers. Use the back of a spoon to press down. Now, spread a layer of avocado mixture over the mangoes. Finally, press sushi rice down onto the avocado mash, using a wet spoon. Press down firmly.
Run a butter knife under water. Run the wet knife around the edges of the measuring cup to release the sushi tower. Carefully invert the measuring cup over a serving plate.
Slowly lift the measuring cup off the plate, revealing the sushi tower. Gently spoon the ahi tuna mixture on top of the sushi tower. Garnish with chopped green onion and additional sesame seeds, if desired.