When you launch StS from your steam library (not from a shortcut) a window will pop up. Select "Play With Mods" and click Play. Alternatively, you can navigate to the game files for StS and run mts-launcher.jar.

Next, a window titled "ModTheSpire" will open up. You should see all your subscribed mods in a list on the left side. Make sure that the checkboxes next to Downfall and all of its requirements are checked. Then click play in the bottom left.

If all has worked, the game should launch after a bit of loading.

I just beat act 4 of downfall, it's so ridiculously fun!

From my experience, you just get the base mods and Downfall, run StS on Steam with mods (you should be prompted do either run the base game or with mods) and include Downfall into the list