Well a warning means that an actual tornado was picked up on the radar or seen and was called in by the weather service station, so the warning is worse than your average thunderstorm warning. But it doesn't necessarily mean its on the ground. Tornadoes themselves are a bit... finicky. Kinda random. If you live in a rickety house or apartment I'd be a little nervous, but you don't seem too concerned by the hurricane so you should be fine unless its a really big tornado, which if it was the NWS would be blasting it on every radio and news station.
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