I'm assuming they mean that the soul is moving through time as the point of perspective, but this liniarity of time is an illusion according to this theory, there isnt something moving through time literally. You are currently in existence at all points of your life assuming that the past has gone and that the future is approaching, whichever point your perspective is occuring at it will still seem like this.
If this person is right and the soul is moving through time, then the soul has no influence over the actions of the body, as our future actions are already fixed. Also we can't have free will because the future is already fixed as it is. This therefore opposes many religions, and not atheism.