Strange... Have you tried with no interpolation on the controller? I mean maybe the ragdoll is trying to interpolate towards an interpolated target resulting in "double interpolation". When using Normal mode, animation following actually lags a frame behind just because in Unity the Animator updates after the physics so there is no way for me to read the pose to follow before the next frame. What do you have for "Normal Mode" in BehaviourPuppet? Do you have your puppet in flat or tree hierarchy and do you have interpolation on the pelvis only or all muscles?