Batting out of Order?
 

Happened in game I was watching 15-18 year olds...

R2. 0 out. Batter sqaures to bunt on first pitch, takes strike one. Bunts strike two foul. Offers at third pitch for K, plate umpire says he went, however R2 is stealing on play and is caught in rundown between 2nd and 3rd, eventually tagged for the out. Batter who K'd doesn't leave and proceeds to step in and continue his at bat. However plate umpire doesn't realize this and thinks it's a new batter. Batter flies out, third out of the inning. After discussions with both managers, and official scorer, the offensive manager argued that the batter is considered to still be at his original at bat, the umpire determined that this was batting out of order. Called the batter who was suppossed to be up out, and had the following batter lead off the next inning.

Is this correct?

Yes, it is correct.