The buyer can only leave one review per purchase, it's not one review per payment.

What is the logical distinction between purchase and payment? How does one know the differences when the transactions are anonymous?

Each step in the transaction flow appends a new step - digitally signed - into a JSON document that acts as a ledger. So the seller puts out the listing and the buyers signs it and sends the funds. The seller won't proceed with the order until the payment is made in full, so the ledger doesn't get any new information until then. The final step (the review) is the last addition to the ledger.

It's based on the concept of the Ricardian Contract by Ian Grigg, adapted to become a ledger. This allows trade to continue asynchronously.

Every purchase goes to a unique address. Multiple payments can be made to that address but they constitute a single purchase.