Each payment is actually a collection of blockchain transactions.
Here is how it works:
[Transaction 1]: You send Ether to our smart contract
[Transaction 2]: You decide to cancel the payment, so you make the cancel transaction to the contract.
[Transaction 3]: The contract sends Ether back to your wallet.
Three separate blockchain transactions occurred, over the course of one payment.
Note: Each of these individual transactions can be viewed on sites like Etherscan too.