In Monero, like other cryptocurrencies, the transactions themselves are fairly instant - they get instantly broadcast to the network and get placed in the tx pool. Wallets also see these transactions pretty much instantly.
A transaction however is not deemed confirmed until it has been mined into a block. And even then, because there can be small reorgs on ...
Each Monero transaction contains multiple inputs/outputs. It is not expected that you own all of the outputs of the transaction; only those destined for you.
The utility you used is reporting:
This address owns output 1 with pubkey: 238a...48ce for amount: 0.297602
Which indicates that your address did, in fact, receive 0.297602 XMR.