Not Your Everyday Play

[EsqUmp]

Here is a variation of an interesting play I recently heard.

1 out. R3 on 3rd, R2 on 2nd and R1 on 1st. Batter hits a line drive to the short stop (no infield fly + 2nd out). F4 catches the ball but drops it in the transfer. The plate umpire immediate states and repeats, "That's a catch, the batter's out." R3, who was off with the pitch, stopped when the ball was hit, but then continued home without tagging up. F4 throws the ball to F2, who stands on the plate and catches the ball before R3 arrives. R3 crosses home plate; however, F2 doesn't tag R3. Instead, F2 throws down to F6, who is covering 2nd base and tags out R1, who was trying to advance. The base coaches throw their hands up in the air and the defense leaves the field.

What is the plate umpire's responsibility of addressing what happened at home plate? What is the call/mechanic. How would you make the call?