The reverse martensitic transformation proceeds through several sub-processes at various time and length scales. We recently studied the transformation kinetics in the large thermodynamic driving force regime. We induced a rapid heating pulse in a shape memory alloy wire and tracked its evolution by multi-frame time-resolved X-ray diffraction at synchrotron radiation with simultaneous stress measurements. The study identified three stages occurring at different times on the microsecond-scale and at different length scales. Specifically, the transformation was shown to occur initially in a thin layer near the surface, and only later in the bulk of the wire. Herein, we explain the obtained experimental results by modeling the evolution of the phase transformation using a continuum approach. Theoretical approaches are discussed and model fitting to experimental results provides insight into the kinetic relation between the velocity of the phase front and the driving force. Results support a scenario in which a cylindrical phase front propagates inward along the wire radius. The propagation of such a high-specific energy front releases energy faster than low-energy fronts forming under low driving forces.