Rule on catching a ball between 2 players

Question
I just watched a high school girls' softball game.  One play in the game was interesting to me and I wanted to see if the umpires had it correct.  
There was a girl on second base with either one or no outs.  A bloop pop-up went out to the second baseman who tried to catch it but it went off her glove and the center fielder caught it.  The girl on second went back toward the bag at second, but didn't go all the way to tag.  When it went off the 2nd baseman's glove she went to third.  The umpires called that the batter was out since the ball never touched the ground, but said that the runner didn't need to tag up at all.  I don't understand why she wouldn't have to go back and touch the base since the ball never hit the ground and they did catch it between the two of them.  I know that a person can tag up once the first fielder touches it on the first attempt, but is the umpires' call to the girl on third correct that she didn't have to go back and why is that since the ball was caught?

Answer
Hi Tim,

a bobbled or deflected batted ball that is eventually legally caught does not allow the runner not to tag up, however as you state they may leave the base as soon as the ball is 1st touched by any defender.

If R1 left the base before the ball was touched by any defensive player they would be liable to be called out on appeal.  It would be incorrect that no tag was necessary on the 1st touch.

Mark