Some products, like an outboard amplifier, or a projection screen have 12 volt triggers on them. These are 12 volt INPUTS into the device. When 12 volts is applied, the power turns on for the amp, or for a screen, the screen drops from the ceiling.
Some products, like A/V receivers or projectors, have 12 volt OUTPUTS. The output turns on (puts out 12 volts) when the receiver or projector turns on. Typically the connection is a 1/8" mini-mono plug between the two items - 2 wires. If your XM radio is triggerable by 12 volts, then you can use the 12 volt trigger on your A/V receiver, if it has it, to turn on and off your XM radio only when the receiver is on.