When an Aspect starts the game with a Minor Power in its hand, does that Minor Power count as a Unique Power (e.g., for Tell the Old Stories)?

When an Aspect starts the game with a Minor Power in its hand, does that Minor Power count as a Unique Power (e.g., for Tell the Old Stories)?

No, it's still a Minor Power.
The type of a card never changes, no matter where it starts the game. If you're ever unsure which type a Power Card is, check the back of the card.