Rinse the sushi rice thoroughly under cold running water using a fine mesh strainer until the water runs mostly clear. Transfer the rice to a saucepan, add the measured water, and cook according to the package directions until tender. While still warm, gently fold in the sugar, rice vinegar, and salt, taking care not to mash the grains.
Line an 8×8-inch pan with parchment paper or plastic wrap, leaving overhang on the sides for easy removal. Press the seasoned rice firmly and evenly into the pan, compacting it well so it holds together during frying. Cover and refrigerate for at least 2 hours to fully set.
While the rice chills, prepare the tuna. Slice the tuna into thin strips, then finely dice into small, even cubes for a clean texture. Transfer to a bowl and add the sriracha, kewpie mayonnaise, tamari, sesame oil, green onion, and sesame seeds. Mix gently until evenly coated, then refrigerate to keep chilled and fresh.
Once the rice is set, lift it from the pan and cut into 18 rectangles. Heat the oil in a skillet over medium-high heat until shimmering. Arrange the rice pieces in a single layer without overcrowding and fry for 3–4 minutes per side, turning carefully, until golden brown and crisp. Transfer to a wire rack to drain and maintain crispness.
Alternatively, brush both sides of the rice lightly with oil and air fry at 400°F for about 20 minutes, flipping halfway through.
To assemble, top each crispy rice piece with a slice of avocado, about 1 tablespoon of the spicy tuna mixture, and a few jalapeño slices. Finish with extra sesame seeds and serve immediately, with soy sauce or tamari on the side if desired.