How can the IMac screen light up while I am away from the house

VikingOSX wrote:

Depending upon mouse sensitivity, a sleeping Mac can be awakened by heavy truck traffic outside reverberating vibrations to the surface below the mouse. I have observed that here, so not Sci-Fi.

IIRC, one of the fairly recent macOS versions (macOS 13?) removed mouse and trackpad movement as a trigger, and now a button press on the mouse or trackpad or a keyboard keypress is required.

Put your Mac to sleep or wake it - Apple Support

For the question more generally, Power Nap is a fairly common for awakening (and as has been mentioned in an earlier reply):

Turn Power Nap on or off on Mac - Apple Support

One of the following shell commands might find some clues about the cause for the awakening, too:

pmset -g log | grep ' wake' 
log show --style syslog --last 1h | grep "Wake reason" 

Your iMac screen can light up automatically for a few reasons even if no one is home. Common causes include scheduled tasks like Time Machine backups, Spotlight indexing, software updates, or notifications. If “Wake for network access” is turned on in System Settings > Energy Saver (or Battery/ Power Adapter on laptops), your iMac can also wake when it receives network activity such as file sharing or Find My Mac pings. You can check Console for wake events and adjust Energy Saver settings to prevent this in the future.

A brief power failure followed by the return of power, can startup the iMac if "Start up automatically after a power failure" is checked in the Energy Saver preference.

Was the machine off or just sleeping when you left?

If it was off and there was a brief power interruption and you had it set to restart in the event of power loss that could account for it.

When you're away from the machine for an extended length of time shut it down. Also what it down at night. Shutting down and rebooting clears out system and application temporary cache and swap files. That can keep the machine lean and mean.

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

I pull the plug out of the wall, when I shut down my iMac!

I know there are divided opinions on this matter, here on this Apple Community!

But it works for me.

Depending upon mouse sensitivity, a sleeping Mac can be awakened by heavy truck traffic outside reverberating vibrations to the surface below the mouse. I have observed that here, so not Sci-Fi.

Unplug your iMac from the outlet. 🔌

That’s how I do it.

No one can scam you if it’s unplugged (I caught a scammer in person claiming otherwise to my face (he turned around and walked away)). 🤨

Good luck! 👋🏼😉

Probably have not experienced this since I retired my 2013 iMac with Mojave on it. The 2020 iMac sitting next to it running Monterey and now Sequoia has never experienced any mouse jitter wakeups — even with the street being ripped up and repaved in the last three months with heavy construction traffic.