Finite-size effects in molecular dynamics simulations of phase transitions are commonly attributed to interactions between a growing phase and its periodic images across the simulation domain. We show that a geometric interpretation is incomplete under nonequilibrium conditions. Molecular dynamics simulations of solidification processes show that for near-equilibrium conditions, a geometric limit can be found where a spherical solid cluster will reach the boundaries of the cubic simulation domain, changing the rate at which the solid phase grows. However, a model based on the resulting reduction in interfacial area does not capture the resulting rate of change, indicating that the effect cannot be explained by geometry alone. Instead, we observe that under rapid cooling, the phase transition continues beyond the geometric limit without an immediate change in slope in the evolution of the phase fraction. The change only occurs when the nonequilibrium transformation trajectory approaches the equilibrium transformation pathway. These results demonstrate that finite-size effects are also governed by the evolving thermodynamic state and free-energy landscape, with periodic face interactions modifying the transformation kinetics. Thus, geometric criteria based solely on domain dimensions are insufficient for predicting finite-size effects in nonequilibrium molecular dynamics simulations. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory (LLNL) under Contract No. DE-AC52-07NA27344, release number LLNL-CONF-2024445.