We present an analysis of the positions and ages of young star clusters in eight local galaxies to investigate the connection between the age difference and separation of cluster pairs. We find that star clusters do not form uniformly but instead are distributed so that the age difference increases with the cluster pair separation to the 0.25-0.6 power, and that the maximum size over which star formation is physically correlated ranges from ∼200 pc to ∼1 kpc. The observed trends between age difference and separation suggest that cluster formation is hierarchical both in space and time: clusters that are close to each other are more similar in age than clusters born further apart. The temporal correlations between stellar aggregates have slopes that are consistent with predictions of turbulence acting as the primary driver of star formation. The velocity associated with the maximum size is proportional to the galaxy's shear, suggesting that the galactic environment influences the maximum size of the star-forming structures.