One thing to keep in mind is that Central Florida weather channels and the National Weather Service use extremely high resolution radar. They can tell the difference between heavy rain, wind, wind shear, revolving storm cells. Everything.
A Tornado Warning is issued when the NWS computer detects revolving cells that COULD produce tornados. They are not tornados until they touch the ground. Funnel clouds are seen when the revolving storms begin to lower and build a little. These do not always turn into tornados.
The high resolution radar can fairly accurately detect problem cells, the direction they are moving, and their heading.
On a national map, "Orlando" is a general term for most of Central Florida. Local maps and radar show the 30 mile distance between Orlando and WDW.
Watching for most of today, there were no concerns for WDW property directly. There were some confirmed tornados around, as close as Kissimmee, but none heading towards WDW.
It is good to hear that WDW takes these seriously. We have been to Typhoon Lagoon during the normal afternoon thunderstorms. They do clear out the pools, but they seemed very lax about the whole situation.
Ted