Do you have the datasheet for the USB module? USB is simply a serial interface, for which you can use my RPi::Serial module.
You need the communication specification so you know how to set up the serial interface, as well as what you need to send to the unit to trigger high/low states of each relay on the board.
I've never even heard of a USB relay breakout board before, let alone used one, but I do have vast experience communicating over USB/serial to dozens of other device types, which is why I stuck with the GPIO scenario.
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