I think they disabled links for people who have very low post counts. Just to prevent spambots from linking to dangerous places. Just standard stuff.
We can still see the url. Don't worry.
That gif seems a bit stuttery.
Again, I'm not sure about the rules that Mecanim follows regarding its execution order.
I'm not sure if we can remedy the one-frame delay but there's probably something that can be done about one-frame pose popping up.
Your repro project seems to have had an unrelated problem that was causing the first frame to pop up.
There was a NullReferenceException because you were trying to call _skelAnimator.Update();
where _skelAnimator was null.
Adding a null check seems to have eliminated that first frame problem.