It took me a while to figure out how soft selection might create this effect. It only influences multiple meshes if you have set to Global mode. Changing it to the standard "Volume" or even "Surface" mode should make it behave more normally. There's two things that are still odd about your video. 1) I don't remember any soft-selection coloring to indicate that it was on 2) Undoing shouldn't undo the influence separately from undoing the move. Either way, glad you figured it out.