What is SetAnimation in your first code? Those parameters are not what AnimationState methods take. It is better to show what AnimationState methods are called. Why is your first and second code so different?
It is also better to paste the code text, not images.
It's not clear why your first video animates the head to be very thin briefly. Is that what you are trying to avoid? Should work like this:
animationState.SetAnimation(0, "walking", true);
// Then later:
TrackEntry entry = animationState.SetAnimation(0, "notice", false); // Maybe pass 1, if you want it on top of "walking".
entry.MixDuration = 0; // Only need this if your AnimationStateData has a default mix duration.
Your second code uses different tracks (1 and 0). I'm not sure this is what you want. You might play walking on track 0 and notice on track 1. Or you could play them both on track 0.
You can try it in Skeleton Viewer, which might help you understand what is going on:
Skeleton Viewer
