Well yes that's technically true but that's not the kind of effect I meant.
After the interaction your become part of the same quantum system and that affects what you can observe next.
When you become a system where the state is a superposition of "electron spin up + you see an electron spin up" and "electron spin down + you see an electron spin down" then you when you observe the electron in spin down you'll always see the electron as spin down because, you guessed it, the "you" in this story is the "you see an electron spin down" you of the superposition of yous