Doesn't really sound odd. It actually sounds like a dust devil acting like a typical dust devil.
Dust devils do stay stationary you know when there's no wind to move the actual funnel.
Ps. The dust devil likely wasn't "chasing" you the fact that you ran away made a small vacuum of air that caused it to move. Same as if you ran away from a floating feather, the feather would "chase" you.
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