The main effect of an electromagnetic wave is basically that the electric field in the electromagnetic wave shoves charged particles around (ions and/or electrons). That's called "Electric dipole coupling". Electric dipole coupling is almost always much stronger than other effects of the electromagnetic wave. For example, the electromagnetic wave has a magnetic field too, which can exert forces on molecules. This "magnetic dipole coupling" is a much smaller effect than the electric dipole coupling.
Shoving an electron around (the electric dipole coupling) does not directly change or rotate the electron's spin. It only changes the spin a little bit, due to "spin-orbit coupling", an effect related to special relativity (in the "rest frame" of the moving electron, the electric fields get converted to magnetic fields, which torques the spin). Therefore, since spin-orbit coupling is a weak effect (unless the electron is traveling near the speed of light), the coupling between electromagnetic waves and molecules cannot usually involve a change of spin. That means that a spin-singlet molecule absorbing light almost definitely goes into a spin-singlet excited state. Conversely, it is exceedingly unlikely for a spin-triplet excited state to emit light while changing into a spin-singlet ground state.
By the way, another possibility is for the magnetic field of the light wave to directly torque the spin of the electron. This effect is normally even weaker than the effect of the wave via the spin-orbit effect.