There are no time delays or anything of the such.
This is how it works:
Buyer is given deposit information.
Buyer goes to bank and makes a deposit.
Timestamp on the deposit slip is matched against the price in the market at the minute the deposit was made to establish the price per BTC. There is no way to abuse the system as you have said.
That is a very nice feature. Currency fluctuation is one of the risks I have to account for on localbitcoins, because some buyers will try to exploit price changes in just that fashion. Where are you pulling historical market data from -- is it the price on a particular exchange or a weighted average?