Just because you woke up while you were spinning doesn't mean the spinning woke you up. The act of spinning will only wake you up if you already believe it will wake you up. So be careful of how you think when trying to figure out dreams. Ordinary logic does not apply.

You might have woken up because your REM was ending and you were already heading for a brief awakening. It's easier to get lucid near the end of a dream when you are already in the process of waking up.