It sounds like the problem is with the TV, inputs are still active when the screen is off? See if there's option in the TV settings to change that? Nothing wrong with the soundbar, which doesn't have a power command of its own.
Edmund Roku Community Streaming Expert
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Please be aware that turning off your TV will not stop a Roku device from streaming. It's always best that when done streaming, you make sure to press the Home button on you Roku device, then turn off you TV.