Question on power of usb cigg light adapter

When the doors are locked and all power is supposedly killed, does the USB adapter plug (cigg adapter) light ever go off? My light stays blue still even with doors locked. And with it plugged in, will it drain your battery overnight?

Anybody has experience with this?
All my other cars, the blue lights goes off when car is off.

I have the Toyota charging kit that came with the car.

Yes it turns off after about 10 min.

Thanks man!