Spin of an electron is measured as a magnetic property. You should not visualize it as an electron "spinning" around its axis, which is what you seem to indicate if I'm not mistaken. Electrons are considered to be point particles. Also, the spin of an electron never changes instantaneously. For example, changes in the electron's spin in the Stern-Gerlach experiment is a dynamical process due to the coupling of the magnetic moment due to the electron spin to the inhomogeneous magnetic field of the Stern-Gerlach magnets. The change in angular momentum of electron spin is compensated in the magnets.
Most importantly, it is important to realize that instantaneous is meaningless in QM, since this can never be accurately determined. To determine a change in a system requires two measurements, which themselves take time to complete. In this way it is impossible to say when things "exactly" occurred. That being said, in QM you can determine the time-scale over which the dynamics occurs.