Apps installs in Sandbox show up in original volume
 

Exerpt from User Guide:

"Maintaining a Sandbox It’s important to remember that applications installed into the “System” folder – /Applications – are specific to the volume you’re running on. If you install an application while running from the Sandbox clone, that application will not be available when running from Macintosh HD."

This is where I can't understand why it isn't applying to my set-up.
When I reboot to my original volume the app that I installed in sandbox-/applications shows up in the original volume when I am led to believe it shouldn't.

This kind of defeats the purpose of the sandbox being a safety net.

Why is this so?

Was the application you installed already installed, and you updated it through a link? There's no "magic" here -- /Applications is a normal folder on the Sandbox, so if files are stored in it, they're not going to magically move to other drives... or shouldn't! :)