Any umpire should do everything he can to enforce the notion that he is an unbiased, neutral observer. Fraternizing with players, coaches or spectators should be kept to an absolute minimum beyond casual pleasantries and communications necessary to relate game information.
An umpire "coaching" a player, trying to tell her how to play her position or offering "pointers", is a cardinal sin. The umpire should not be making comments on the player's performance or play.
There are a hundred little things an umpire can do that might give the appearance or perception that he's favoring one team or the other, from chit-chatting with the base coaches, to accepting an offer of a drink of water from one team or the other, to being overly eager with retreiving loose bats or equipment for the players, to standing in one dugout or the other to get some shade on a particularly hot day.
And, certainly, the plate umpire leaving his position to "celebrate" with a player standing on third base would fall into that category!
Why shoot yourself in the foot? You'll find enough trouble on the ballfield as it is, without going out of your way to look for it. Anything that gives one team the impression that you might be showing favoritism toward the other is just asking for trouble.
CONQUEST07, on the play you asked about:
- There is no such thing as a "one second rule". If that's what the umpire told you, he needs to brush up on the rules! There is a "Look Back Rule" that could apply here, but there's nothing in that rule about "one second" being any sort of a time limit.
- Despite the name, there's nothing in the Look Back Rule about the pitcher having to actually look at the runners when it is in effect.
- If, as you stated, the runner from third base was "off the bag and moving toward home", she hasn't violated any requirement of the Look Back Rule- at least not yet.
- If the pitcher "threw the ball in the air", then she obviously did not have possession of it while it was in the air. If the pitcher does not have possession of the ball, the Look Back Rule isn't even in effect and you can't call a runner out for violating it!
What is the right call? Hard to tell from the information provided. It depends on the timing of what the runner from third did and if the pitcher was holding the ball when she did it.