Sorry for late reply, I have been away for a christmas trip.
TNManager is located in my startup scene, yes. It is attached to the same gameobject as where TNAutoJoin is attached. TNAutoJoin joins another scene where the actual game content is. (Just like your multiplayer tutorial with dedicated server).
I don't recommend synchronizing position and rotation using TNAutoSync when using mecanim motions. Sync whatever causes the motions states to change, or the changed states themselves. This way each client will have an up-to-date set of states and do their own movement logic.
I am not talking about incompatibility with TNAutoSync and Mecanim. I understand that TNAutoSync is generally not good for syncing your "main character". I am talking about that I believe it's impossible to structure my game objects like you mentioned:
Rigidbody, TNObject
- Collider 1
- Collider 2
- GameObject with LagPosition (and possibly LagRotation) on it
-- Renderer
Apply root motion will cause the "GameObject" to move relatively to the "Rigidbody", in such way the Rigidbody itself will not be affected by the Mecanim's movement. The colliders will stay in the same fixed global position while the GameObject with the attached animator will move around. The problem I'm facing is that I don't know how to tell Mecanim to apply root motion onto the Rigidbody instead of the GameObject.