I don't follow. A specific kathisma is appointed to be read every midnight office (either IX or XVII). Are you saying that these kathismata are part of the continuous reading of the psalter?
I'm sorry, my recollection was hazy. Those kathismata are in the midnight office independent of the continuous psalmody. I confused their use in the midnight office with the reason for the shuffling in the psalmody that occurs after Vespers on Thursday evening. Up to that point, starting on Saturday night, they are read straight through from 1-15, but then they are read in this order: 19, 20, 18, 16, and 17. See here