While deformation twinning in hexagonal close-packed metals has been widely studied due to its substantial impact on mechanical properties, an understanding of the detailed atomic processes associated with twin embryo growth is still lacking. Conducting molecular dynamics simulations on Mg, we show that the propagation of twinning disconnections emitted by basalprismatic interfaces controls the twin boundary motion and is the rate-limiting mechanism during the initial growth of the twin embryo. The time needed for disconnection propagation is related to the distance between the twin tips, with widely spaced twin tips requiring more time for a unit twin boundary migration event to be completed. Thus, a phenomenological model, which unifies the two processes of disconnection and twin tip propagation, is proposed here to provide a quantitative analysis of twin embryo growth. The model fits the simulation data well, with two key parameters (twin tip velocity and twinning disconnection velocity) being extracted. In addition, a linear relationship between the ratio of twinning disconnection velocity to twin tip velocity and the applied shear stress is observed. Using an example of twin growth in a nanoscale single crystal from the recent literature, we find that our molecular dynamics simulations and analytical model are in good agreement with experimental data.