I have a Windows 10 EDU Anniversary Edition PC with TightVNC 2.8.5 x64 (also tried 2.8.7 posted in another bug report here). I have the Mystify screensaver configured with a 1 minute timeout, and the monitor is configured to power down in 2 minutes.
If I am remotely connected to the PC via TightVNC the screensaver activates in 1 minute as expected, but after 2 minutes the screensaver exits and I'm returned to the desktop as if I had moved the mouse or typed a key. If I disconnect the TightVNC session (but leave TightVNC service running), the screensaver activates after a minute and then the monitor successfully sleeps after 2 minutes.
Previous TightVNC releases did not exhibit this behaviour.
Forgot to mention that if I disable the screensaver, but leave the monitor to power down as before then it works when I'm connected via TightVNC. It only seems to occur when the screensaver is active.