Shape memory alloys (SMAs) are functional materials featuring unique shape recovery properties that make them suitable for key industrial applications. The essential process controlling this fascinating performance is microstructural twinning. Some twin systems are much more frequently observed than others, yet a fundamental mechanistic understanding of this evidence is missing, which hampers SMA design. Here, we consider the prototypical NiTi SMA to show that the emergence of twinning can be strongly affected by twin interface mobility. In this work, we adopt an integrated approach combining crystallographic theory, state-of-the-art atomistic modelling, topological model, and validation with high-resolution transmission-electron micrographs. Atomistic simulations confirm that the occurrence of twins is dictated by the driving force for twin boundary motion rather than interfacial energy. Moreover, our findings settle long-standing questions by elucidating the propagation mechanisms of twin interfaces, which the established martensite crystallography and kinetic theories could not address conclusively. The newly discovered understanding of the role of interface mobility in twin formation can be used to predict variant selection and guide the design of SMAs with improved functional performance.