Assignor Nightmares

[waltjp]

I don't think I've ever been suprised by an appeal. You can usually hear the players and coaches talking about it as soon as playing action stops. Also, keep in mind, with a dead ball appeal there's no need for the pitcher to throw over to the base - he, or anyone else can simply request the appeal.

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FED 8-2 Penalty

(clipped)
A dead-ball appeal may be made by a coach or any defensive player with or without the ball by verbally stating that the runner missed the base or left the base too early.
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I wasn't there but it seems pretty obvious from the OP that there was no intent for the defense to appeal the missed base until the PA announcer chimed in. For that matter you might conclude that the PA announcer only added his 2 cents because he felt his team had missed something. There must have been some time elapsed if the announcer had a chance to view the replay.