Only basing this on my experience with other tense situations - I've never had to shelter from a tornado at Disney.
However, I would think that a theatre full of guests taking cover from a tornado would actually be a fairly upbeat, positive crowd. People will be trying to make it seem like a fun, exciting adventure for the kids, and that kind of attitude spreads quickly. There would be a lot of laughter and positive comments and generally cooperative behaviour. People will be looking for guidance from castmembers, and I'm quite certain Disney has briefed them on what they need to do (ie, pass out cookies, put on a movie, etc).
Vacationers in general, tend to be a fairly happy bunch.
Things won't get ugly until the crisis passes and people start lining up at Guest Services, looking for their compensatory Grand Floridian Upgrade.