If you turn the radio off before you turn the ignition off it shouldn't turn on when you start the engine. This is the only use for the radio button I can see. for all else I either use the touch screen or the steering wheel controls.
There has been a number of upgrades. When I brought my THP156 in for its first service I told my Dealer that there were upgrades. They didn't seem to be aware of this as an issue as ter weren't anybulletins from Peugeot Australia. The Dealer checked it out and had me come back the next week to install the upgrade after they had received it from Pug Oz. I recommend that you check this out with your Dealer. I'd check that there isn't some weird menu option that forces the radio on on start up first but even if there is I believe that you should always have the latest firmware.