That said, it isn't obvious to me why causation would be necessary for consciousness.

How about "consciousness is computation, and causation is necesary for computation".

Say we simulate your brain and record the simulation. We then divide the recording into 100,000 pieces, scramble them, and put them back together. Then we play the recording. The Dust theory says that the recording will be conscious just in no way proceeding along the arrow of time the way we are. Is the recording still a causal system?

Yes. But who ever said that any old causation is necesary for consciousness? Both computationalism and phsyicalism say consc.is a particular kind of causal process. The causation of playing back a simulation is not the causation of generating it in the first place.