Glad you ask.
How can you guarantee the finalisation of trade if you don't escrow bitcoins?
We check all the bitcoin transactions using our bitcoind node and DB that we created from bitcoind database (similar to blockexplorer or ABE).
The user need to register his bitcoin address and provide a proof that he really is the owner of the address.
He can provide the proof by signing a message using a private key belonging to that particular bitcoin address.
Next we simply check the transactions in blockchain and pair them to trades on BitStock exchange.
Why sellers should send bitcoins after closing a trade if price of BTC rise?
Good question. We solved this by something that we call a "refundable sales deposit".
The seller needs to deposit a "refundable sales deposit" on his/her BitStock account to be able to sell bitcoins.
If the trade is closed and the seller suddenly decides not to send bitcoins, then this sales deposit is withdrawn from his account as a penalty and deposited to the buyer.
The seller has strong incentive to really send the bitcoins. However if for some reason bitcoins are not sent then buyer will receive the sales deposit as indemnity.
You can find detail explanation here
https://www.bitstock.com/info/selldepositrules.