MASSIVE SECURITY PROBLEM - Genie Logs Into Neighbor's Router

Your wireless devices connected to his router, not yours. You wired device connected to your router. The 'security breach' was on his end. Probably an unprotected SSID and the signal was stronger that your SSID and the wireless devices connected to his signal. Look at your wireless devices and see what SSID it is connecting to, and IF it even sees your SSID.

You didn't detail what your wireless devices are? If Windows PC's or Laptops, you can get Acrylic (https://www.acrylicwifi.com/en/wlan-software/wlan-scanner-acrylic-wifi-free/) install and run it and you can tell what SSID's and thier power and channels are around. I doubt his SSID is the same as yours but it could be on the same channel and stronger signal.

If you are worried he can connect to you, check YOUR router log, it should show (if enabled) who is connecting by IP Address and MAC Address. From your post it probably only is your PC.