it does take a while to get a tall phlox to expand like this but once it gets going yummmm

I allow mine to self propergate by cutting spent flowers and tucking them into the middle of the stems as the leaves wilt I add a handfull or two of there garden soil with the leaves and tap it in to the base
I then let the stems stand as is untill 2 inches of leaf is seen in springcreating new stems I then cut the old stems and dig it up and seperate it into sections of size of four or five each and return them with in division back into garden.. You can do this divison into a 2 quart pot as well.
I would assume your method looks correct but a guess would be concidering rotting hormone as it is a step for cuttings on different own root growers

from one single tall phlox I got 3 stalks taking two years years the following year I got 5 stems on the forth 3 more every year after I now get an avg 6 stem from three second generation talls in two different but close spots next spring I am going to say yummmmmmmmm I predict a total of 36 which will all get a 5 to 6 stalk split from the second generation stems and 6 from the inital one which will get split into 3 stalks

good luck on your efforts on propergating that way