Stairs are complex ...
Also, creating the STAIR OPENING, creates a framed opening in the floor ABOVE the stair, so that wouldn't have had any effect.
Typically I create the stair on ALL floors, and then turn off EXTRACT IN MODEL for the ones that don't apply. I also use CTRL to COPY the stairs to the clipboard - Change the layer to of the highlighted stair to HIDDEN - and turn it off, then paste (HOLD IN PLACE) the staircase back to the default layer - EXPLODE the staircase, and create the relevant stair geometry with lines.
The lines show the staircase location on plans and don't show on the model, and the HIDDEN layer staircase shows in the 3D model, but doesn't show on the plans.
As has been mentioned before, BE CAREFUL pasting staircases in place adjacent to exterior walls that are differing thicknesses, as the stairs WILL snap to the walls.