Project TXA deploys special smart contracts on each supported blockchain that traders can use to deposit funds. These funds are locked, and any supported hDEX exchange can respect those locked funds as collateral, then essentially on the exchange order book the trader can trade with IOUs. hDEX exchanges trust that the IOUs are backed by collateral, and controlled by the Decentralized Settlement Layer's network of SDOs.
At no point does the hDEX exchange take custody of funds. SDOs reach consensus on a fair settlement by listening to the broadcasted trades.