Do you mean to say that the amp's turn on/remote input may be tied to the ignition and not the turn on signal of the HU ?
In any event, amps do this by their nature. I'm not sure if it's due to the internally stored energy in the transformers or if it's related to the input suddenly switching (you could find out by unplugging the RCAs I guess). The amps that don't (when turning on) have what is called an "anti-thump" feature added which is active for the first few seconds after the device is powered on. The amp's still making the thump, it just does something or other to prevent any noise (signal or otherwise) from going through the subs. Sadly, there is no easy way to give a signal to your stereo that says "I'm about to turn off so please activate that anti-thump thingie" so you will hear it when things turn off.