CB Core Fields Ajax is intended to be primarily used on profile, but yes it can work on userlists. For it to work on userlists be sure to configure it as follows.
Integrations > CB Core Fields Ajax > Userlist
Display: Enable
That should be all that you need to do. Note if the field is not editable it won't be ajax editable either. The Access parameter explains this to you that normal edit checks are still applied. In short if you can't see the field in profile edit you won't have access to ajax editing either.