your amp is probably turning off with the car but it takes a second for the capacitors to drain. so like you said, the radio turns off and that little bit of power left over in the amp is what causes the pop.
Easy fix is to instal a switch to turn the amp off manually. Then just turn the amp off before the car. But that can be a pain
Option 2.... What is your amp wired into for its "remote" on/off? If it is the radio then try to find a system that would only be on if the car were running. The radio will stay on till you open the door so if the amp kills as soon as you turn the key off then you might have enough time between then and the door opening to eliminate the pop.
Last option is what I did when I did lots of car audio. I built a little box that consisted of audio input(s), audio output(s) and a 12V power ground. 12V power was supplied from the same source as remote on/off for the amp. The 12V power was used to activate a relay in the box. When the relay was active (closed), audio was allowed to pass through the box. However, when the car is turned off (and thus the amp) the relays open very quickly and prevent any signal from passing to your speakers. This is what I did to eliminate pops in the past and had great results. There may be something that you could buy now days but when I did this for a living about 5 years back that was how we did it. Sent from AutoGuide.com Free App