What method should I use to create an association between the recurring payment and the customer?
There isn't one. As far as APIs are concerned, the APIs for QuickBooks and the APIs for QuickBooks Merchant Services are entirely independent, and they don't really "interact" with each other in any way.
It would be your application's job to maintain an association between the QuickBooks customer, and the stored "wallet ID" for the credit card information and scheduled billing information. It would also be your application's job to actually push a record of the credit card charge over into QuickBooks for each transaction (e.g. QuickBooks Merchant Services just charges cards, it doesn't push any info into QuickBooks automatically).
We have some wiki info on QuickBooks Merchant Services integration APIs on our website.
You can then look into the QuickBooks Online APIs (either Intuit Anywhere or the QuickBooks Online SDK to push the data to QuickBooks.
It seems like I am speaking of reconciliation
Not really. Reconciliation is the process of matching up the payments you recorded in QuickBooks, with the money that actually got deposited into your bank account, less the fees. You can't even do reconciliation without first making the charges and getting the data into QuickBooks somehow.
It's might be worth looking into software out there that is specifically geared towards what you're looking to do - I know at least ChargeOver does recurring billing and integrates with QuickBooks.