Cook rice according to package directions. Transfer to large bowl; stir in vinegar, lime zest, salt and sugar. Let cool completely. Refrigerate for 1 to 2 hours or until well chilled.
Shape 1 tbsp rice into 2-inch round; transfer to parchment paper–lined tray. Repeat with remaining rice (you should have 24 rounds).
Heat 1/4 cup oil in large nonstick skillet set over high heat. In 5 batches, cook rice rounds for 3 to 4 minutes per side or until golden brown and crispy, adding oil to the pan as needed. Transfer to paper towel-lined tray.
Meanwhile, in shallow dish, combine white and black sesame seeds. Pat tuna dry with paper towel; roll in sesame seeds to coat.
Heat oil in large heavy-bottom skillet set over high heat until smoking. Cook tuna for 1 to 2 minutes per side or until seared and sesame seeds are golden. Transfer to cutting board; let stand for 5 minutes. Slice thinly into 24 slices.
In blender, purée avocado, mayonnaise and lime juice until smooth.
Top each crispy rice round with seared tuna, drizzle of avocado mayonnaise and jalapeño slice.