Start Selling With Vimeo On Demand from Vimeo Staff on Vimeo.
Video on Demand Selling Handbook.
One of the features of Vimeo's Video on Demand is a advanced stats dashboard. From there you can track among other things, promo code redemptions.
So if you assign a different promo code to each of your affiliates, you'll be able to tell how many sales are generated each month by each affiliate.