[sterner, now, because that is a dangerous train of thought] The dimensional stabilizer could kill everyone here instantly. It could fill the dome with methane. It could turn you into a potato. It could make you believe that you have lived your entire life in a well or that you are your own mother. But it could not send anyone home. None of you are connected to those dimensions any longer.
Your memories apply to infinite universes that exist parallel to yours. It is a romantic notion that they still bind you to the world you left behind, but speaking in a quantum sense, this is your world.