Dunno if you ever figured this out but going to mention same text that is within the readme:
Remember to launch the game through mod's provided launcher.
Launching the game as normal results in double speed game.
Viewing post in Nuclear Throne Ultra Mod comments
I just grabbed the mod, and whether I launch it inside Steam, via a Steam Game Icon, or directly by double clicking the EXE in its directory via File Explorer, it's double speed. Also, even when applied to the itch version I have of the game, it attempts to launch the Steam version of the game, oddly enough. I thought I could fix this by temporarily uninstalling my Steam version, but it then still launches the Steam client (just not the game itself).