They were standing over the lake so he drowned the night before when he went back and was in the lake when the training exercise happened. No one saw the body and because the Ice guy froze the lake his body was never sent back.
She stood over the pond with him and said this is where he died. Then he teleported back in time, right on top of the water and drowned. Now white hair guy doesn't even remember the conversation they had because teleporting dude died before it happened.