<snip>
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!
In a P2P platform like bisq, the money never gets locked away, infact the exchange does not have access to it since they changed the way escrow works and stopped being a party in it.
Now the escrow address is a 2-of-2 multi sig, from the 2-of-3 is used to be, and the only parties involved in it now are the traders. Technically the funds still remain in your custody until the end of the trade and the platform has no access to it.