How to make external display go to sleep after xx mins?
As a first step I would reset both your NVRAM and SMC, as well as double check your Energy Saver settings.

Resetting the NVRAM on an early-2016 12" MacBook model

Follow these steps:


Shut down your machine. Yes, a full shut down, not just logging out.
Press the power button and then press the commandoptionpr keys. You have to make sure you press these keys before the gray screen appears or it won’t work.
Hold those keys down until your Mac reboots again and you here the startup chime.
Let go of the keys and let your Mac reboot normally.


Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).

Resetting the SMC on an early-2016 12" MacBook model


Shut down your computer
Keep the power cable plugged in.
Press at the same time shiftoptioncontrol (on the left side of the keyboard) and the power button
Let go
Turn your computer back on with the power button.


Energy Saver Settings

You don't specify in your question how you've configured your Energy Saver settings, but you may want to double-check what you've actually set under the Power Adapter tab. I've come across many instances where MacBook users forget that there's two tabs you can configure.