A three-dimensional numerical model is developed to investigate the influence of sulfur content on the transitions of thermo-capillarity and flow dynamics during laser powder bed fusion (LPBF) of 316L powders. The impacts of variations in sulfur contents on thermal behaviors involving heat transfer and solidification characteristics, thermo-capillarity transition, as well as the spatial and directional transitions in flow dynamics, are analyzed through mechanistic modeling techniques. It is observed that transient thermal behaviors, including melt pool profile, track morphology, and solidification processes, are significantly influenced by the contained sulfur concentration. High sulfur concentrations tend to result in finer microstructures and equiaxed grains. Through simulations, it is noted that the transition in the sign of temperature coefficient of surface tension (TCST) is more easily observable in low-sulfur level (0.0001%) but disappears as the sulfur concentration is extremely low. With sulfur content increasing, a more homogenized velocity distribution is observed, accompanied with heightened flow complexity denoted by the emergence of additional branch flows and vortices. These findings offer valuable insights into the underlying physics of melt pool dynamics in the LPBF process and present a potential approach for process optimization.