Re: First Replicator Usage?
It could be that the tribbles get into the machinery of an automated central food preparation room/complex located at one or more locations of the starship, through an air vent, and got beamed into the food slots in the mess hall from there.
"The way that you wander is the way that you choose. / The day that you tarry is the day that you lose. / Sunshine or thunder, a man will always wonder / Where the fair wind blows ..."
-- Lyrics, Jeremiah Johnson's theme.