I'm very much not an expert but I do know it works.
I assume it is because the SSH tunnel originates locally and that is how the traffic is funnelled from the static IP on the VPS to the machine on the local network. Like a VPN or Tailscale or something.
Ah, you tunnel from the home machine to the VPS and then back and forth from it maybe? I was thinking about it from a remote point of view where you wouldn't be there to 'do stuff'.
I still don't understand how you're going from the linux box to your machine if your machine's IP is changing/hidden.