If I have a Serene Ascetic on a battlefield and I hide Tornado Warrior there. If my opponent uses a spell and targets my Serene Ascetic, when I react and flip my Tornado Warrior to empower Serene Ascetic, does my opponent have to pay extra because of the empowered ability of Serene Ascetic?

No — your opponent doesn't owe anything extra for the spell that's already targeting Serene Ascetic.

Deflect's extra power is a mandatory additional cost paid while the spell is being played (CR 809.1.d, 356.2.a.2), and the cost is locked in at that moment — once the spell is on the chain, gaining Deflect can't retroactively add [A] to it. Your Tornado Warrior's "when you play me from face down, you may empower something here" is a triggered ability that goes onto the chain above your opponent's spell, so it resolves first and the Ascetic really is Empowered before their spell resolves — but that only affects spells and abilities played after that point.

So the practical upshot: their current spell resolves normally, and any later spell or ability they play this turn that chooses Serene Ascetic costs [A] more. Note the empower only lasts until end of turn (Tornado Warrior disempowers it in the Ending Step), and the Shield 3 half of the Empowered ability only matters while she's defending in combat, not against a spell.