Stairs are temperamental things. The main fix is to always place the stairs before building walls. Secondly, always place the bottom stairs before the top stairs, as in work your way up. Thirdly, and most importantly for you, the tiles forming the top entrance of one set of stairs and the tiles forming the bottom entrance of the other set of stairs can never ever overlap. It won't allow you. I hate that, but it's how the game limits the staircase functions.
EDIT: My third point is invalid according to the referenced guide. My sincere apologies.