First I've ever heard of a Crutchfield phone person being clueless like that without checking with their techs.

I've never owned one of these things. But if it were me designing the device, I would design it so that the last thing that was powered-on would take precedence. No flickering back and forth, that would be bad design.

And if it had the ability to play both of the devices, that would mean it was a mixer instead of a relay. It would actually be really cool if it did that. But I doubt it.