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Say we are having a swimming race and both leave the same starting side at the same moment. I get to the other side of the pool and return to the starting position before you reach the opposite side of the pool. Just because I lap you doesn't mean I travel back in time.

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Ok, that makes sense, but what happens to the light being emitted from your internal ship lighting. Are you traveling faster than that? How do you look around?

It's relativity; internal lighting will look the same because light in your ship will still be traveling at the speed of light relative to you (if I'm not mistaken).

the wikipedia article linked above talks about this, saying that the "...This method of transport does not involve objects in motion at speeds faster than light with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move faster than the ship. As objects within the bubble are not moving (locally) faster than light..."

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