What happens if the on-chain transaction fails (with funds returning to the ASP)?
Ark transactions are atomic (via Anchored transactions) so if the ASP’s on-chain transaction (aka Round tx) fails, Bob never received his VTXO. Just like with Bitcoin, Bob only has a UTXO after Alice’s payment is confirmed.
VTXO’s are Bitcoin transactions that spent a part of an existing UTXO.
Having said that, Alice can send a VTXO to Bob instantaneously, by sending him a OOR (Out Of Round) VTXO. In this case, Alice is forfeiting to Bob the right to spend a part of an existing UTXO, i.e. Alice is forfeiting her VTXO to Bob.
The disadvantage of OOR VTXOs for Bob is that Alice (colluding with the Server) can double spend her VTXO, so there is trust involved. Bob can fix this by trading this OOR VTXO for a VTXO in the next round.
VTXOs are completely trustless, Bob can anytime broadcast it to mainchain and get a UTXO.
Know more about Anchored transactions, VTXOs and Ark in general here:
https://joaobordalo.com/labs/ark/