Also wondering how they discern that you are eligible for 10% back on the award miles.
Eligibility is determined by having an open and active eligible Citi / AAdvantage account at the time of redemption.

Use of a qualifying card to pay the fees?
Your Citi / AAdvantage account must be open and active at the time of redemption but you are not required to charge AAdvantage Ticketing Service Charges for an award flight to the Citi / AAdvantage card to earn this benefit.

Specific link to book award travel (similar to Citi reduced mileage awards?)
Just book your award travel as you normally would and your bonus miles will post to your AAdvantage account 6-8 weeks after your redemption.