A small concept I'm a tiny bit confused about. Sakurai in the introduction to quantum mech introduces the Stern Gerlach experiment. According to his discussion, an $S_{x}+$ particle that goes into a SG apparatus with $B\hat{z}$ will split 50-50 into $z+$ and $z-$ directions.
However, if we consider time dynamics of the state, Sakurai says a $S_{x}+$ state will start to precession and the expectation value of $\langle S_{x} \rangle \propto \cos\omega t$ and $\langle S_{y} \rangle \propto \sin\omega t$
My question is this: Is the spin precession only valid when the spin is under the action of the magnetic field? Once the spin exits the magnetic field, shouldn't it split into $z+$ and $z-$ with basically no knowledge of whether or not it was precessing?