do you mean jk near the corner air throw?

I don't think I've gotten an air throw on an opponent after a jump kick hits them when they are on the ground. Not saying its impossible, I just haven't gotten it.

Do you think its possible they could have jumped right before it connected? If the jump began right before the kick hit, you wouldn't really be able to tell except that no blood would come out off of the jump kick.

I'll have to try the teleport->air throw some time, I never tried that.

EDIT: I can't get forward teleport punch->air throw to work. In the corner its not hard to get jump kick, forward teleport punch, then land and jump and get an air throw. But the damage after the teleport punch is crap.
And then there's poor Sheeva. You can get Jump kick, jump kick, teleport punch, throw on her easily. Easily enough that theres probably a lot more you can do there against her.

In MKII Jax could do a JK backbreaker on a grounded opponent, but this was removed in MK3.

As for air throws, I think it's the same rule in both games, self controlled upward/off ground movement of the player is required before you can get it. It's hard to air throw on the way down and if they are moving away due to collisions.