There's a race condition in AbstractConversationContext when create first conversation scope if it's the first request of one session.
Suppose such scenario

1. User request a jsf page
2. weld create a conversations map in the AbstractConversationContext.associate()
3. Because it is the first request, there's no session. Weld keep this map in request
4. Then somewhere, a session is created
5. In the render phase, server sends piratical response back. The page need some jsf resource, eg, jsf2 ajax or resource
6. Browser request the new jsf resource
   At this time
   The first request has not finished. So it doesn't reach dissociate() and doesn't put conversations map in the session.
   Meanwhile
   The second request reach associate(). There's no conversations map in the session, and the session is existing. It puts its new map! <====

Then, even the first request finishes it's response and reach dissociate(), because there's already a map, it doesn't put its owner anymore. <====

A quick and dirty fix is always create session before associate(). However, it's better to merge the map in the dissociate()

Such page reference a conversation scoped bean