This is completely normal. The "shutdown" procedure only shuts off power to the main PC, but it is unable to control the power switch located separately on the monitor. Software cannot flip a hardware switch.
However, this is a good thing as well. The monitor, when detecting "no signal" from the computer, will put itself to sleep in a very low power state. It uses such a small amount of power, you'd have difficulty measuring how much is used. However, by using this small amount of power, it is able to turn itself back on faster when you power on the computer.
My monitor has an orange light that stays on when there's no power, which turns blue when I turn on the computer. Perfectly normal.
Hope you enjoy the new system!