From the article : "after the first inning, Alfonso Marquez, the home-plate umpire, asked him to remove the dirt so there wouldn't be any question about any controversy."
Well, that doesn't even say Marquez looked at his hand.
I'm not taking any position on whether or not there was something there. I'm agnostic on that point. As a Yankee fan, I can afford to be bemusedly detatched.
But I didn't see any video of any umpire inspecting Kenny Rogers' hand. The fact that he was not inspected and told to turn out his pockets means somebody did not do his job, and that somebody is Tony LaRussa. If LaRussa wants to imply that Rogers is dirty, but is unwilling to back it up by requesting and inspection, then that is where the problem is.
After the first inning would be when Kenny Rogers was coming out to take the mound for the Top of the Second. Unless I am mistaken, he washed his hand after the Bottom of the First, when he went back to the dugout and the Tigers came up to bat. Since the game is in Detroit, he would not have had to stick around to bat.
So after the First, before the start of the Second, Rogers' had would have already been washed.
Rogers denied any umpire ever asked him to remove anything.