As for Big D's Ice Climbers, he played pretty much the same way he does at his locals. Big D missed a lot of grabs and damage from those. In one of his games, he got a landing n-air at 0% but lost a lot of damage because he did not convert it into a grab. Big D played well but he can work on his edgeguarding more by using Blizz Wall (Blizzard desyncs) to easily cover the ledge with one Climber and use the other to punish roll in, or any other option the opponent may have chose.
In the Exodia set, match-up inexperience carried Big D. Exodia respected Blizz Wall too much (which resulted in him standing there not punishing Ice Climbers), and Ice Climbers in general. Add to that, the hype in the venue gave Big D a leg up. He only used desynched F-throw to f-air once, but he did get ledge trump > f-smash a few times. A lot of clips where the community popped off and Tylor on Twitter posted clips, were just basic Ice Climbers stuff that the people in attendance were unaware of. As for the Captain Zack set, he grew a brain in Game 2 and that was when Big D started to fall apart.
Some Ice Climber players say that Big D is just a good player who uses desyncs as he see fits, and I can see that.
Edit: Oh, and as for that teleport during one of the games, that's been in since Day 1, I've heard it called the Squall Glitch. No clue exactly why this happens but all I know is that you have to use Squall Hammer during a match to set it up.
Edit 2: Big D usually makes it grands at his locals. He is good at putting on a show. You guys can find at least 2 grand finals of him vs LetsTickle, an Inkling player.
Edit 3: I said that Big D, landed a F-throw to fair desynch, but in fact he did not (watching the set now and that part just happened). He just did Down throw to f-air which is not true if you DI away from Ice Climbers. Last time I brought it up in the server, I was told that Down throw to f-air is never true, so I guess Exodia must of thought it was so that's why he did not try to escape it.
Edit 4: Big D used Squall Hammer so much and his opponents let him get away with it. The move is punishable but it does autocancel or lowers the recovery frames if you do mash the move and the Ice Climbers leave the ground. This does not increase the damage of the move.