Firstly, I suspect the message actually says that "Monitor is in Power Save Mode - Activate using PC"
That usually indicates that the PC is either not turned on or that the PC has crashed or failed to boot, but the monitor has been powered up.
When the PC turns "off", that is sensed by the monitor which then also goes to sleep. The message will usually be displayed if the monitor is powered up when the PC itself has not sent it a wakeup signal.
The message is produced by the monitor itself, not the PC.
Similar thing here if there is a power cut, the monitors come back on with a message, as they have been powered up again without the PC having put them in sleep mode and then awoken them.