Do you have to pay the extra power for ambush units in the new Mystic Vortex battlefield during showdowns?

Yes. When you play an Ambush unit to a battlefield where you control units during a showdown at Mystic Vortex, you must pay the extra [A] (1 Power).

Here's why: Ambush (Rule 822.1.b) grants the unit "I have [Reaction] as long as I'm being played to a battlefield where you control Units." Mystic Vortex doesn't care whether the word Reaction is printed on the card — it checks whether the card has the Reaction characteristic. Since the Ambush condition is met, the unit has Reaction at the time of play, and the cost increase applies during Step 3 of determining total cost (Rule 356.3).

This works the same way as Hidden cards at Mystic Vortex — Hidden grants Reaction as a characteristic, Ambush grants it conditionally, and Mystic Vortex treats both identically.