Public silence, yes, and to his players, yes. Today, though, I think LaRussa will be talking to some baseball officials privately. Either way, though, Rogers is on public notice, so to speak. He would be very foolish to risk using pine tar the next time he pitches.
Cordially,
I doubt he has been silent with the players. And I doubt he'll make any "private" inquiries about it. Like I said, he's been around the block a few times. And he most likely knows a good deal about the past hundred years or so of baseball and pitching.