Have you heard of people completing the trades at there end by saying the money was sent and it wasn't? Just had this experience with someone they confirmed with localbitcoins that the money was sent (this was last Friday - September 26th) and I still don't have the money in my account. I tried contacting the trader for confirmation numbers from the deposit so my bank can start looking for the money and he won't respond. Now I have to file a dispute with localbitcoins as I never received payment. I don't understand people, why waste my time and your own? If you can't afford to purchase the bitcoins, then why not be upfront and honest and say so?
Never release the bitcoin from the localbitcoins escrow unless you have checked it yourself that you received the payment.
In your case, just ask that trader to provide the proof that he has sent you the money. If he doesn't respond or can't show the proof, you should win the dispute for sure.