The expanding doesn't necessarily mean moving, the distance between gravitationally unbound objects is increasing, but those objects aren't "moving" in the classical sense because at some point they will be "moving" faster than the speed of light, which is impossible. So I think within this discussion, If you were to build a time machine that would disappear at one time and reappear in the same coordinates, You wouldn't end up in a void your galaxy "moved" while you stayed stationary, your Galaxy stayed in the same "place" just the space between the galaxies increased in size. But from your galaxy's frame of reference the other galaxies that are not gravitationally bound are moving. Which movement in the universe depends on your frame of reference so conversely the other galaxies would see you moving away also. But you didn't "move" relative to those galaxies, though you may have moved relative to the surrounding galaxies that you are gravitationally bound to.