It sounds like your system may be set to Sleep or Hibernate instead the assumed Shutdown.
If this is so, then that would explain why the USB ports are still on as they are used to wake the system such as with your Mouse or Keyboard.
One way to deal with this would be next time you shut the system down, pay close attention to what you are doing instead of just habitually clicking.
Select "Start > (This next part Should read Shutdown but may in fact read Sleep or Hibernate"
If it reads one of the last two, select the arrow to the right and a list will pop up allowing you to select Shutdown. You can change this permanently by right clicking on the Taskbar > Select | Properties > Start Menu tab. Here you can change the Start Menu Power Button action to Shutdown.
This way when you shut your system down, the USB ports won't be waking your system up any more.
The other option would be to go into the Control Panel > Power Options.
On the Left side, you'll want to select Create a Power Plan.
Now mine is already setup and I don't want to risk messing it up, so I'm not going to click that particular link on my system. But I can tell you what to expect.
After you create your Power Plan which is usually fairly basic and you save it, Go back to the Power Options and click on the link to the right of your Power Plan, - Change Power Settings > (Next ignore the two buttons here) Select - Change advanced Power Settings, A dialog box will pop up with a bunch of advanced settings. This is what you will truly want as it will allow you to control most every aspect of your systems power settings including the power button on the front of your system.
Hope this is of some help