The steps below do get wet as you're coming down, but you are getting that up quickly, before anything has a chance to be absorbed. I use very low pressure when doing stairs and so there really isn't much in the way of overflow. That said, it's always a good idea to have an absorbent towel at the bottom of the steps if it isn't carpeted. I do come back thru with a stair tool for the backing and grooming purposes, and also to get any left over extra moisture. When I'm finished, the stairs look amazing and are left with very little moisture.
ETA: FWIW, Rotovac also makes a smaller rotary stair attachment that fits onto the 360i. I don't use it because it requires more work than it's worth, IMO. Rotovac would do well to come out with a smaller gadget for the smaller piece.