We discuss the origin of young stellar objects recently discovered in the central regions of star clusters of the Large Magellanic Cloud by investigating cold-gas accretion on to clusters through our simulation code. First, we discuss the detection of young populations and their correlation with cluster mass and young stellar objects. We show that young populations do not have a mass correlation, but are spatially associated with star clusters. We then create an analytical model of accretion from a giant molecular cloud on to a cluster, and perform numerical simulations of the gas evolution of the Magellanic Clouds during tidal interactions. Our simulations find that interactions between the Magellanic Clouds can greatly increase the amount of H2 available to clusters, allowing some to accrete greater quantities of gas, but cold gas accretion alone cannot explain the presence of extended main-sequence turn-offs in low-mass clusters with young stellar objects. The variation in accretion histories between individual clusters is dramatic. We find the amount accreted is primarily defined by cluster mass and the relative velocity between the cluster and interacting molecular cloud. The gas mass fraction, metallicity, and the strength of the tidal forces are all important parameters. Finally, we explain our results by comparing them with observations and propose observable consequences of our model.