Since many readers here probably don't have access to the Major League Baseball Umpires Manual, which is the primary source of this mechanic:
8.7 "VOLUNTARY STRIKE"
In the situation where the third strike eludes the catcher on a half-swing and the batter-runner is entitled to run to first base, the appeal should be made to the base umpire instantly (without waiting for a request from the defense); but even if the appeal is not instant, the appropriate umpire should immediately and voluntarily make the call of strike IF the base umpire is going to reverse the plate umpire's call. This will give the batter the immediate opportunity to run.
[Capitalization and bolding verbatim from the MLBUM]
Note that this is very slightly different than #4 listed above, in that a voluntary call by the BU should only be made if he is going to rule a strike.
As far as I know, FED and NCAA haven't published any mechanic to be used in this situation, but IMO this should be applied in all codes.