EDIT: Confirmed, Mind Flower requires level 13 Harmony and you have to be in the city screen when you build it (you can't build it from the main map production menu because you have to select a tile to build it on).
I noticed the same thing. I built the mind stems well before I built the flow and it didn't actually seem to lower the time required at all, at least I don't believe it did. I was at 25 turns until win the whole time and the turns just went down naturally. I wish the numbers were more available to us, because as of right now I can't tell if the stems actually do anything at all.