ABSTRACT We simulate the formation of second-generation (SG) stars in young clusters with masses of 105 and $10^6\, \mathrm{M}_{\odot }$ within $30\!-\!100\, \mathrm{Myr}$ after the formation of clusters. We assume the clusters move through a uniform interstellar medium with gas densities of 10−24 and $10^{-23}\, \mathrm{g\, cm}^{-3}$ and consider the stellar winds from asymptotic giant branch (AGB) stars, gas accretion on to the cluster, ram pressure, star formation, and photoionization feedback of our stellar systems including binary stars. We find that SG stars can be formed only within the $10^6\, \mathrm{M}_{\odot }$ cluster in the high-density simulation, where the cluster can accrete sufficient pristine gas from their surrounding medium, leading to efficient cooling required for the ignition of SG formation and sufficient dilution of the AGB ejecta. Hence, our results indicate that a denser environment is another requirement for the AGB scenario to explain the presence of multiple populations in globular clusters. On the other hand, the ionizing feedback becomes effective in heating the gas in our low-density simulations. As a result, the clusters cannot accumulate a considerable amount of pristine gas at their centre. The gas mass within the clusters in these simulations is similar to that in young massive clusters (YMCs). Hence, our studies can provide a possible reason for the lack of gas, star formation, and SG stars in YMCs. Our results indicate that the ionizing stellar feedback is not a severe problem for SG formation; rather, it can help the AGB scenario to account for some observables.