I've said this many times before, I just discovered it through much play:
when both players are using their tornado on each other, the winning player (the player who will go through his/her opponent's tornado and damage the other MK) is the one who started his/her tornado most recently. For example, if you use your tornado and then try to come attack me, I can then use my tornado and collide with yours, resulting in your tornado being negated (tornado disappears and you're left to be punished) and my tornado being the one to deal the damage.
Also, the same rules apply if you are fighting a Kirby and he has stolen your tornado ability, the last tornado made wins.