Unity 5.1 networking sync player animations

I'm trying to understand the new networking infraastructure in Unity 5.1, and made a simple scene with a network manager spawning a ThirdPersonController prefab (that is in the Characters package).

I've updated the ThirdPersonUserControl script to inherit from NetworkBehaviour and do input evaluation only when isLocalPlayer is true. I added NetworkIdentity and NetworkTransform components to the prefab. NetworkTransform.TransformSyncMode has options for Sync {None, Transform, Rigidbody2D, Rigidbody3D and CharacterController.

When I choose Rigidbody3D and use a Local Host and Local Client, I can see the character move and be affected as a Rigidbody, but without any animations. I thought syncing CharacterController would fix it, but there's no movement at all if I choose that.

The prefab comes with a Third Person Character script, which doesn't receive any messages, but is called from the Third Person User Control script. It handles the animation updates based on movement. I'm not sure if I should be [SyncVar]'ing all the members and such.

Sorry for rambling. My question is: What's the right way to ensure player animations are sync'd in a multiplayer scenario?