In a small bowl, gently fold the rice vinegar and sea salt into the warm cooked sushi rice until well combined, then allow it to cool to room temperature.
Prepare the fillings by slicing the sashimi-grade tuna into long, thin strips and peeling the cooked shrimp if necessary.
Julienne the cucumber into thin matchsticks and slice the avocado into thin wedges.
Place one nori sheet on a bamboo rolling mat, shiny side down.
Wet your fingers slightly to prevent sticking and spread half of the sushi rice evenly over the nori, leaving a 1-inch border at the top edge.
Arrange half of the tuna, shrimp, cucumber, and avocado in a horizontal line across the center of the rice.
Using the bamboo mat, firmly roll the nori from the bottom up, tucking the edge over the fillings and continuing to roll until the top border is sealed.
Repeat the process with the second nori sheet and remaining ingredients.
Using a very sharp knife dipped in water, slice each roll into 6-8 even pieces.
Serve the rolls immediately with pickled ginger, wasabi paste, and tamari for dipping.