Windows 8.1: Keep remote monitors/displays off during RDP

I know it's on old question, but I had the same problem and found why it is happening. I found out that it's "by design" on this website https://docs.microsoft.com/en-us/windows-hardware/design/device-experiences/modern-standby-wake-sources

Remote Desktop can turn on the display on the target system.

And during my testing, I found out that during Remote Desktop connection monitor indeed wakes up, but it goes to sleep after X minutes, and those X minutes are that which you configure in Power Options "turn monitor off after X minutes of inactivity" (or something like that, I don't have English Windows).

I'm not sure about making windows do this, but you could try an old technology approach & turn off your monitor.

That would solve your issue.