We study the dynamics in optical collisions of Na with Ne, Ar, Kr, and Xe in a differential scattering experiment. We report the observation of nonadiabatic transitions in the excited collisional quasimolecule based on measurements of the population ratio of the Na(3p)P-2(1/2) and P-2(3/2) fine-structure levels. Comparison with theoretical results shows a generally very good agreement over the range of collision energies (0.01-0.3 eV) scanned in our experiment, using the best available potentials. For the heavier rare-gas systems a strong influence of the B Sigma-A Pi crossing on the population ratios is observed. We further extract a universal function for the nonadiabatic transition probability for these systems. In the thermal energy range, our results are in good qualitative agreement with data from gas phase optical collision experiments.