The Jungian reading
The tornado is affect organized into a system — not just anger or fear but a self-sustaining spiral of them: a family conflict, an addiction, a mental state that feeds on what it destroys. Its apparent intentionality is the point: the dreamer experiences the chaos as aimed. Shelter-seeking is the dream's real plot — where you hide, who is with you, what the storm takes — and maps the actual coping strategy with its actual gaps.