Hi, I am trying to finalize my first transaction at localbitcoins.com , it would be in person and in cash

The seller 'claims' that the transfer is instant, no waiting like a wallet to wallet

I want to know if in fact that is true, and if so, should i be aware of any risk. Like say he transfers to my account at localbitcoins.com and I see it there, is there any risk at all there could be a problem with his bitcoins at that point?
and is he correct that normally when dealing with wallet to wallet (outside of localbitcoins.com) there is in fact a delay of even up to around an hour) but there isn't any delay when moving from 1 account at localbitcoins to another account.

thanks