To disable remote assistance press the windows key + break or start --> settings --> control panel --> performance and maintainance --> system, to open the system properties. You can then turn remote assistance off by selecting the remote tab and deselecting the remote assistance options.
This could alternitively be a Wake on LAN problem, what type of connection do you use to connect to the internet? If you're going through a router it might be causing the PC's to turn on for some reason. There should be a setting in your network adapter properties to disable it.
Try disabling remote assistance first and post back if it still happens.