Given that you see them 'Jack-in' via a jack at the base (more or less) of their skulls, I would guess that the jack short-circuits the regular neural process, although possibly routing the data to the Matrix system, in case of relevance. (I.e., the machine uses the sensory feedback to identify issues that may occur with the real body, such as loss of fluid in the pod. Possibly it sends limited neural commands BACK to induce twitching in the muscles, to keep atrophy from getting TOO excessive; note that people pulled from the pods are weak.. but not as atrophied as you would expect from a life time of no movement.)
That being said, I don't know that the revolution uses the exact same technology; if they are simply stealing it and re-purposing it, it may function in the same way. We do see physiological info on the users when they are jacked in, so it's not unreasonable to assume that the data is being passed; it would then be up to the system it's being passed to to determine how much, if any of it, to pass back up the line to the user's brain. Based on their lack of response when Cypher is interacting with their 'real' bodies, it seems likely that their system, too, captures all local data and doesn't pass it back to the brain.
I would guess that this also explains why disconnecting someone before they 'Jack-out' kills them; the circuits are still in Interupt mode, passing data along the jack, not from the body to the brain. Jacking-out resynchronizes them to each other. Failure to jack-out before losing the connection results in a loss of data flow from the brain to the body, which, among other things, would result in a ceasing of the heartbeat, breathing, and so forth, causing death very quickly.