What Rick was referring to is this:
The Phaeton recognizes who the driver is by looking at the key that is used to start the vehicle. In other words, the car can store up to 8 different sets of individual driver preferences (you, your wife, and your 6 teenage kids), assuming you are willing to buy an additional 5 keys, in addition to the 3 keys you got with the car.
Once a driver (key) is recognized, the car calls up all the saved preferences for that driver. This includes the radio volume start-up setting. If you have the radio volume start-up setting adjusted to the lowest possible level (only one bar visible on the far left end), the start-up volume will actually be 'OFF'. This is probably the condition you have at present.
To get all this driver recognition from the key fob working, it is necessary to once only match the key fobs with the driver preferences stored in the infotainment unit. Chances are that your VW dealer already did this for you as part of the PDI process, so, you can likely ignore that reference that Rick made. But, if you want to double-check that everything has been set up right, here is how you do the checking:
Find the three keys. If you have keyless access, make sure that only one key is within 25 feet of the car at any time. If you don't have keyless access, you can have all three keys with you (on your person) all the time.
1) Lock the car, leave it alone for 2 minutes.
2) Unlock the car, put the key in the ignition, turn the ignition on (you don't have to start the car). Check the driver ID screen that comes up on the infotainment display - just after you dismiss the legal warning - to see if the owner of the key you used in the ignition matches the list of driver names on the screen.
3) Turn the ignition off, get out, lock the car, wait 2 minutes, repeat the process with the next key.
If it appears that the car is not correctly matching up driver identification on the infotainment screen to the different keys, then refer to this thread for complete instructions about how to set it up: Store Settings for the Seat Memory buttons, key fobs, driver preferences (a complete how-to guide for setting up a new Phaeton).
FWIW, I do suggest that Phaeton owners identify the keys by using different key fobs or whatever, and then ensure that the principal driver (owner) always uses the same key fob, and the secondary driver (spouse, partner, significant other) always uses the other key fob. This will really, really simplify life for everyone. It is, of course, possible for anyone to use anyone else's key fob at any time - the car will still work great - but the driver who is using someone else's key fob will have to manually recall their stored preferences by pressing the button on the outboard side of the driver seat (to recall preferences for 'things that move'), and by manually identifying themselves to the infotainment system (to recall preferences for 'things that don't physically move').
To give you an example - if you drive out to the airport with your wife, then you get out to catch your flight, and your wife gets into the driver seat to take the car home, she has two choices: a) Turn the car off, give you your key, and then start the car with her key (kind of clunky), or; b) leave the car running with your key in it, but manually press the button on the side of the seat to recall her preferences for 'things that move' (seat, mirror, steering wheel, etc.), and then go to the appropriate menu on the infotainment and press the soft-key beside her name to recall her preferences for 'things that don't move' (radio stations, temperature settings, suspension settings, radio turn-on volume, and so forth).