Using large-scale kinetic Monte-Carlo (KMC) simulations, we investigate the non-equilibrium surface growth of the fullerene C60. Recently, we have presented a self-consistent set of energy barriers that describes the nucleation and multilayer growth of C60 for different temperatures and adsorption rates in quantitative agreement with experiments [Bommel et al., Nat. Comm. 5, 5388 (2014)]. We found that C60 displays lateral diffusion resembling colloidal systems, however it has to overcome an atom-like energetic step-edge barrier for interlayer diffusion. Here, we focus on the particle-resolved dynamics, and the interplay between surface morphology and particle dynamics during growth. Comparing C60 growth with an atom-like system, we find significant differences in the evolution of the surface morphology, as well as the single-particle dynamics on the growing material landscape. By correlating the mean-squared-displacement of particles with their current neighborhood, we can identify the influence of the different time scales that compete during growth and can pinpoint the differences between the two systems.