Preheat a grill to medium high. Pierce the steak all over with a fork. Combine 3 tablespoons each ponzu sauce and wasabi mayonnaise with the vegetable oil in a large bowl. Add the steak; turn to coat. Let sit 10 minutes. Meanwhile, cook the rice as the label directs, adding the ginger to the cooking water.
Brush the grill grates with vegetable oil. Remove the steak from the marinade; add the scallions to the marinade and set aside. Grill the steak, 8 to 10 minutes per side for medium rare. Transfer to a cutting board and let rest 5 minutes. Meanwhile, remove the scallions from the marinade and grill, turning, until charred, about 3 minutes; transfer to the cutting board.
Fluff the rice with a fork; discard the ginger, if desired, and stir in the sesame seeds. Toss the cucumbers and carrots with the remaining 1 tablespoon ponzu sauce and the vinegar. Thinly slice the steak against the grain and roughly chop the scallions. Top each serving of rice with the cucumber-carrot mixture, steak, scallions and the remaining 1 tablespoon wasabi mayonnaise.