Should I shuffle my deck after every Dazzling Aurora effect taking place?

Yes, you must shuffle the cards revealed by Dazzling Aurora before placing them at the bottom of your deck.

According to Tournament Rule 421.8:

"When two or more cards are recycled to the player’s Main Deck as part of a single action, the above procedures 1-7 [shuffling/randomization] should be followed for that group of cards to properly randomize them before recycling them."

How it works with Dazzling Aurora:

1. Reveal cards from your deck until you find a unit.
2. Banish and Play that unit.
3. Shuffle all other revealed cards together.
4. Place that randomized stack at the bottom of your deck.

Important Nuances:

• Random Order: An official FAQ confirms that when 2 or more cards are recycled simultaneously (like with Dazzling Aurora), they must be placed at the bottom in a random order, which requires shuffling them.
• Opponent's View: Your opponent is allowed to see all cards revealed by the effect for a reasonable amount of time, as they are considered public information during the resolution.
• No Burnout: If you reveal your entire deck and find no units, you do not burn out. You simply shuffle all the revealed cards and put them back as your deck. Burnout only occurs if you are forced to draw from an empty deck.