The Antidote should work the same way as Folktails.

From analysing the code, and watching them in game... they Drink an Antidote. It cures 12.5% Contamination, this fills the Antidote need half-way, so they'll drink up to 2 at once.
Then they have to wait until the Antidote timer runs down before they can drink another antidote.
The need drops by 1 per day.
So it takes 8 antidote and at least 3 days to cure a beaver.

oh ok, i thought it was almost instant, i spent 2 days trying to get them cured, but it didnt seem like they drank any

FWIW, I have seen Leaf Coats drinking the Antidote and it being effective so if you're still having problems, try re-verifying the game files from the Steam Library. Also, do you have any other mods installed?