If you want to cross a note to the staff above or below without changing the voice it’s in, use N/M (Edit > Cross Staff > Cross to Staff Above/Below) rather than moving or duplicating the notes to the staff above or below.
Moving/duplicating to the staff above or below basically automates cutting the note from the original staff, then pasting into the new staff, so it uses the first voice on the destination staff, just like regular pasting does. This is absolutely as intended.