Yes it's wired up to a permanent live supply, instead of an ignition controlled circuit.
Radios have two supplys one permanent, to maintain memory, and one via ignition switch for actual radio
If you turn the radio on with the ignition off it stays on for and hour. If you turn it on with the ignition on, it should switch off when you turn the ignition off and back on again when you turn the ignition on next time.
Some radios have a user selectable option to continue for a preset time after turning off the ignition.
The radio in my firm's Pug van can be set to continue playing for 0, 5 or 20 minutes