It takes two to tango.
The water does what water does... it falls from the cloud.
The wind is already circulating because the top of the cloud is still rising and drawing in air. There are very complicated winds in the cloud but we do know it is drawing in the air. All rain clouds do that.
Then the tornado falls from the cloud. You can see the vids of the tornado coming down out of the cloud. The funnel does not rise from the ground, it begins at the bottom of the cloud and drops to earth.
In that funnel is cloud matter: water. The wind is barely visible, but the funnel, being full of water, is quite visible. Or am I the only one who sees this? It seems I am..... 
The strongest part of the vortex is that which is being displaced by the water which is in the funnel of water falling. The winds gain force as the water hits the ground and spreads out, like the upside down T.
It's a dance of wind and water. Wind going up, water falling down.
Edit history
= new reply since forum marked as read