We have a turn style staircase too. We had the carpet installers use the same rug material as the rest of the rooms.
In our staircase there is 5 steps that turn. Count how many steps that turn on yours. It is always an odd number of stairs!
What they did was bound the edges and used one piece for the lower part of the starircase and another one for the upper part of the stair case. They the stapled the runner to the stairs. For the turned steps. They used 2 pieces for each stair. One piece they put it on top of the stair and then stapled it on the sides and underneath the edge of the satair and the 2nd piece they put it on the face of the stair and stapled it on eth edges and top and bottom where the pieces meet. It came out beautiful!!
Since turned stair cases are difficult you have to watch that it is straight and does not "bubble" out and that is is straight and in align wuith the top and bottom pieces (not crooked)!