CMON would still be responsible for running and fulfilling its own Kickstarter campaigns, but once a Kickstarter is complete, any remaining product would enter the distribution chain via Asmodee NA.
One odd thing about this deal is that in December 2018, CMON announced that it had entered into distribution agreements with GTS Distribution and Southern Hobby Supply, so that as of January 1, 2019, U.S. retailers would be able to order CMON titles from these distributors in addition to getting them from ACD, Alliance, and Peachstate Hobby Distribution. Asmodee, however, has an exclusive distribution deal with Alliance Game Distributors — a deal put into practice in August 2017 — so after only a few months of carrying CMON titles, GTS and Southern Hobby Supply lose access to those titles once again, with ACD and Peachstate also having the CMON lines cut from their catalogs.
While this change in distribution practices might seem like a radical departure from previous practices, it's not out of the ordinary as in many European countries one of the branches of The Asmodee Group is already distributing titles from CMON Limited.