In many physiological situations, BAR proteins interact with, and reshape, pre-existing curved membranes, contributing to essential cellular processes. However, the non-equilibrium and timedependent process of reshaping, and its dependence on initial membrane shape, remains largely unknown. Here we explain, both experimentally and through modelling, how a BAR protein dynamically interacts with mechanically bent lipid membranes. We capture protein binding to curved membranes, and characterize a variety of dynamical reshaping events depending on membrane shape and protein arrangement. The events can be generally understood by an isotropic-to-nematic phase transition, in which low curvature templates with isotropic protein orientation progress towards highly curved lipid tubes with nematic protein arrangement. Our findings also apply in cells, where mechanical stretch triggers BAR-protein-membrane interactions that enable potential mechanotransduction mechanisms. Our results characterize and broaden the reshaping processes of BAR proteins on mechanically constrained membranes, demonstrating the interplay between membrane mechanical stimuli and BAR protein response.