My guess is that you are not actually powering down the printer but placing it in some kind of sleep mode. While in sleep mode the printer will appear to be off but will actually be in a low power state. As soon as a fax comes in the printer powers back up to normal and recieves the message. You might want to take a look at your ECO and sleep settings as well as confirm the printer is actually powered down when you press your power button on the front of the device.
Otherwise the simple fixes would be to physically unplug the printer when not needed. You could also remove the phone cable if recieving unwanted fax messages is the primary concern. I'd like to see your printer boot up from a fax message if there are no phone or power cables attached.