When someone chooses to pay you with Velos, the will send you a co-signed transaction (signed by the sender and the Gateway).
As the receiver, you can then validate the transaction (ensure the amounts are correct and the destination is in fact your address), validate the signatures (signed by both sender and the gateway), and then you can also validate the on-chain balances of both the sender and the gateway (to ensure the sender has enough, or at least the gateway has enough reserves).
All of the above can be done very quickly with no delays related to the blockchain (baking time + confirmation). As the receiver, if you are happy with the above you can choose to accept and complete the transaction. Settlement occurs via an on-chain call, where the balances are actually updated.
If you choose not to accept the tx right away, you can instead settle the transaction on-chain, and then wait however many block confirms you want before completing the transaction.