Its picking up a sudden mains surge when you plug it in. You should really have the sub turned off on its amp on the rear of the sub before plugging and unplugging. Once plugged in, you can then turn it on and it should make that sound.
My sub momentarily makes a noise when you turn it on, it's nothing that will damage it. Be carefull not to plug the power lead in when the switch is in the on position, or plug the subwoofer cable in when the subwoofer is on.
Nothing can really hurt it apart from electronic surge, so use a protector for all of your kit.
So do I but the sub still makes a loud pop noise when turned on and off at the back. It always has from new and it's only really had 1 years worth of use. I have never thought much of it, my guitar amp does the same thing.
I find the best way is just to leave the sub switched on and turn all the tv stuff on together at the switch. No noises that way
Most subs use a relay on the poweramp outputs to prevent the switch on thump as the poweramps supply charges and settles down. It's a cheap sub, so it probably doesn't have them and there's nothing that can be done about it unless you stop turning it on or off.