You computer has a feature for Out of Band management. Either WoL as others have mentioned or vPro(Intel), iLon(HP), iDrac(Dell), as well a few other less popular systems depending on who makes your mainboard or NIC.
This leaves the power on to the network card so that it can be used even with your computer off. It does not have access to your normal computer in the this case. Just the ability to turn on/off the system and sometimes options to update BIOS/UEFI firmware and send a console image to either a client or browser.
The lights are blinking because broadcasts packets from other devices on your LAN are sent to every device. This is normal and expected behavior.
I feel like the people who should write an identifier on their body during a hurricane are the same people who wouldn’t bother to listen to government officials advise.