In a decentralized, P2P service, you are always in control of your funds and at no time do you give that up to the exchange or any other party until the trade is done.
So let me get this right, how on earth are you still in control of your funds till the trade is done?
It means the other guy would have to wire you the money and only when you receive those you send the coins?
No, that's not how it happens! The moment you initiate the trade the money gets locked on that platform, and you're not opening trade on any of those without depositing money, which means they have left your control!