No reason to eject here.

Since when does the coach need to call time to argue? LOL I too won't pick on something petty like that. Just gonna make things worse.

I also am NOT going to run away from the play immediately either! When I am making the "big call" I am staying down and staring at the play. Yup, this DOES invite them to come out. No problem. Me staying there or not, if they WANT to come out on me they will, and staying there means less time wasted waiting for the coach to make it across to field towards me. I also think that leaving the position too soon makes it appear that you know you blew the call and are "running away" from it. MANY coaches agree with this perception. Just ask around a bit.

I have no judgement on the call itself. It is somewhat grainy video coming from youtube and the shot is not still to evaluate it well.

As to the umpire moving while the play happened, I think this is becoming more and more "acceptable". You see it all over the place now. MLB, MiLB, D1, etc... I would say half the video shown at last years NCAA Regional Clinic that included a base umpire showed the guy moving, and close to half had the home plate ump moving too! I have mixed thoughts about that. I was chastised by some guys in my college group for suggesting at the 2007 Regional Clinic that soccer referee's have been making calls on subtle things that happen while at a dead sprint for years and getting it right, why can't an umpire make some of the easier calls while moving?

On some calls, I think staying still it adventageous, on others, I think it prevents you from actually SEEING the play. So, it is tough to say when and where you should be moving or set to make calls. I suppose your experience will guide you on that.