Mechanic question

[greg99]

I'm just a parent seeing if this is the correct mechanic (?).

2 Outs no one on.
Batter swings and misses for third strike. Ball clearly hits the dirt before the catcher catches it very cleanly. (nice drop ball if i must say).
I know its a D3K as well as the ump. calls strike 3 and nothing else and leaves his right hand up.
catcher rolls the ball to the cirlce, both teams leave the field.

Now my question.

the ump followed the batter (3-5 feet behind) to the dugout with his hand still up. called her out as soon as her foot hit the dugout.
Should he have followed her or just stayed at the plate?
No one knew she wasn't out, but I'm thinking his actions might have let someone figure it out.
I'm just curious if he did the right thing, the call was dead on, no question the D3K.
Althought alot of parents said, suzy caught the ball. Yea she did, right after it hit the dirt.

Thanks