Since in the OP and the above video the umpire called the batter out after the identical appeal process ( give a new ball to the catcher who then steps on the plate) I have to assume it is a legal appeal in NCAA.
That umpire appears to have messed up also. NCAA rules are completely different than every other softball rule set. When a ball goes out of play, the defense cannot make a dead ball appeal until the ball is put back into play and made live again.