what happens for us more-or-less equatorial types?

Well, the strength of the Coriolis effect depends on latitude, starting with zero Coriolis effect at the equator and reaching its maximum at the poles. Probably, in terms of large features like atmospheric pressure systems, this means the circular shape isn't very circular when the feature is near the equator. (This is party the reason for the doldrums near the equator, I believe.) As for tornadoes - I really don't know. I don't think they're able to form as easily at the equator since they are offspring of a pressure system. And they also don't travel very far (in global terms). I will see if I can find more info and PM you with it.