Bring 2 cups water to a boil; stir in rice. Cover; reduce heat, and simmer 20 minutes or until liquid is absorbed and rice is tender. Stir in vinegar, sugar, and salt. Cover and chill thoroughly.
Drain pickled ginger, reserving 1/4 cup juice. Combine ginger juice and next 3 ingredients; stir well.
Cut tuna lengthwise into 8 strips; place strips in a heavy-duty, zip-top plastic bag. Pour half the juice mixture over tuna. Seal bag. Chill 30 minutes.
Unfold phyllo; cover with plastic wrap and a damp towel to prevent drying. Fold 1 sheet of phyllo crosswise in half; spray pastry with cooking spray. Place nori sheet on bottom edge of pastry. Spoon 3 tablespoons rice mixture across 1 short end of nori. Place 1 strip of tuna on rice mixture. Spoon 3 tablespoons rice mixture over tuna. Roll up, tucking in pastry as you roll. Place on a baking sheet lined with parchment paper. Repeat procedure with remaining phyllo, nori, rice mixture, and tuna.
Bake at 450° for 10 minutes or until golden. Cut each roll in half diagonally. Serve with remaining juice mixture, ginger, and wasabi.
* Nori is a paper-thin sheet of dried seaweed that is generally used for wrapping sushi and rice balls. It can be found in Japenese markets and some supermarkets.