A tornado dream, hmmn, one of my specialties, meaning, one that I've had repeatedly. Gotta love those tornado dreams. They are pretty exciting, that tornado that is always approaching but never quite gets there...meanwhile, you and others are scurrying around looking for a safe place. That's how it happens for me.

But, you got to see the tornado...or dust devil. You seemed to be able to see it realistically enough to know its size and strength. That's a clue.

I seldom see the tornado in my recurring dreams because I'm always looking for the perfect closet, or the best place to hide under tons of heavy machinery in some giant warehouse, or at a lower level in a high rise...etc. etc. But, in my dreams, there is never any glass breaking, any wind flying, any oncoming train sound...just the silly fright.

But, the idea that others are involved, that we must get everyone safe, that somehow we are all seeking shelter from the storm....my dreams, as well, often involve other people around me seeking shelter. That's another clue.

Perhaps the idea that you noticed, that it wasn't just "every man for himself" -- that kind of idea -- that the dog mattered -- that you weren't just running scared. The dream seems to be showing you what kind of person you are, when the chips hit the fan...

  I've also have had a number of tornadoe dreams and over quite a span of time.

They almost always have represented a near and up and coming emotional upset or turmoil period in my life, wherein i will be tested emotionally. 

  Although there were a couple of times wherein they were more literally precognitive and corresponded with an unusual amount and severity of actual tornadoes.  However, these tend to have a different feel.