I'm assuming in college softball that you are not automatically out for touching the next base without touching the previous one, or in this case, giving yourself up (This is true in at least HS baseball.). But if so, the ump should have just called her out when he handed the ball to the catcher.
If not, as I'm assuming, when the ump gives the new ball to the catcher he is saying the ball is dead & the play over. That means he considers the hitter as having given herself up on the play no matter what anyone on her bench tells her to do. Normally that's when the player reaches the bench, but the ump did call it dead before then with his action (Clearly you can't have two balls played on the same live play.)
With the ball dead, there can be no play; i.e., the tag by the catcher, nor can the hitter touch the plate & count as touching. Net, the ball has to first be put in play, the pitcher step off the rubber, and appeal by either walking to the plate & touching it or having the catcher do it.
So the ump was wrong in allowing the tag to count. Whether OM would have executed an appeal play for the out is unknown.