The Late Show is recorded in the late afternoon, so anything that happens on the show becomes public knowledge long before the program airs at 11:35pm ET. So when Dave dropped the retirement bomb late Thursday, there was no way it was going to stay a secret for more than, say, six seconds.
It just so happens that Mike Mills and Peter Buck–you remember them from REM, right?–were on the show backing up musical guest Joseph Arthur. When the Dave made the announcement, one of the first to tweet about it was Mills.
That was followed by this video: