The seller in P2P Exchange Binance has already owned Bitcoin in his/her Binance account and it will just transfer into your account without creating a transaction in the Bitcoin network, that's why you didn't see any transaction in your Bitcoin deposit address in Binance.
You can only see transactions in your Bitcoin deposit address once you sent some Bitcoin there from an external Bitcoin wallet.
@Silhorn, What @GreatArkansas said is true especially when using Binance Peer to Peer Market platform (P2P).
You cannot verify the transaction that happened during the trade in blockexplorer because it is an "
Off chain" transaction which means that the particular transfer of bitcoin into your P2P wallet occurred outside the blockhain itself as opposed with "
on-chain" transaction. That is why the transfer of bitcoin occurred instantly without paying any transaction fees.
However, if you decide to transfer your bitcoin from Binance to any wallet or an exchange, that is the only time where you can see the transaction details using your preferred bitcoin explorer.
An off-chain transaction is the movement of value outside of the block chain. While an on-chain transaction - usually referred to as simply 'a transaction' - modifies the blockchain and depends on the blockchain to determine its validity an off-chain transaction relies on other methods to record and validate the transaction