Prepare sushi rice according to package directions and let it cool to room temperature before assembling the rolls.
If you want smaller rolls, fold stacked nori sheets in half, press to crease, then gently separate to get half sheets; otherwise use whole nori sheets.
Wrap the bamboo sushi mat in two long pieces of plastic wrap so rice and nori won't stick to the mat.
Make the spicy tuna: finely chop the ahi tuna and place in a bowl; add sesame oil, Japanese mayonnaise, and Sriracha, then mix until combined and evenly coated.
Place the bamboo mat on your work surface with the slats parallel to you and a nori sheet on top, dull side up, long edge nearest you.
Wet your fingers and spread a thin, even layer of cooled sushi rice over the nori, leaving about a 1/2-inch strip of nori at the far edge free of rice.
Place a line of spicy tuna along the rice slightly off-center toward you and add a couple thin cucumber slices if desired.
Moisten the exposed nori edge with a little water, then lift the near edge of the mat and roll away from you, pressing gently to form a firm roll; remove the mat and press briefly to shape.
Use a sharp, wet knife to cut each roll into 6 pieces, garnish with chopped green onion, and serve with low-sodium soy sauce, pickled ginger, and wasabi.