Yes, it protects you.
To my understanding, the clause, "if you were to place a cube" implies that it is the last thing to be checked when placing a cube. therefore the quarantine will be checked and resolved first, and then you are no longer trying to add a fourth cube.
I think the wording on outbreaks is just to cut down on fidlliness. In reality you are placing a fourth cube in the city, it's just that it is immediately moved to an adjacent city. It's just easier to say "Add one cube to each adjacent city instead" instead of "Add a cube, but then move it to an adjacent city, then add a cube to each other adjacent city."
To my understanding, the clause, "if you were to place a cube" implies that it is the last thing to be checked when placing a cube. therefore the quarantine will be checked and resolved first, and then you are no longer trying to add a fourth cube.
I think the wording on outbreaks is just to cut down on fidlliness. In reality you are placing a fourth cube in the city, it's just that it is immediately moved to an adjacent city. It's just easier to say "Add one cube to each adjacent city instead" instead of "Add a cube, but then move it to an adjacent city, then add a cube to each other adjacent city."