Start by making the relish and mayo. In a small bowl, combine the cucumbers, onions, cilantro, chile, vinegar, and sugar with a pinch of salt. Let stand at room temperature for 1 hour. In another bowl, combine the mayonnaise, galanga, and lemon juice. Stir to combine and refrigerate until ready to use.
While the relish is standing, mash the chile, and garlic with a mortar and pestle into a paste. Stir in the fish sauce, green onions, and lime juice. Move to the side and dice the tuna into small cubes (about 1/8 inch). Add the chile paste to the tuna and toss with your hands until evenly coated.
Add both oils to a cast-iron skillet and heat to medium-high. Lightly form 4 patties and add to the hot skillet. Cook for 3 minutes on each side for medium-rare.
While the burgers are cooking, toast the buns, and drain the cucumber relish.
Split each bun and top with a tuna burger, bean sprouts, and cucumber relish. Spread 1 or 2 tablespoons of mayo on the top bun and place it on top of the burger.