The generation of acoustic vortices across various spatial domains is crucial for many orbital angular momentum (OAM) applications. Traditional methods, however, are restricted by the conventional OAM conservation law, limiting their capability to generate vortices solely within either transmission or reflection spaces. Here, we propose an approach that circumvents this limitation through a hybrid design integrating a phase-gradient metasurface with an OAM filter. We reveal that asymmetric OAM transition, achieved through the synergistic interplay of OAM tunneling via the filter and OAM diffraction mediated by the metasurface, overcomes the conventional constraints, allowing for direction-dependent OAM generation. This facilitates precise and arbitrary control of spatial energy distribution of generating vortices, leading to the OAM generation in arbitrary transmission and reflection spaces. Experiments are conducted to validate these findings. This work presents an alternative strategy for realizing diverse OAM generation or asymmetric propagation, thereby expanding current capabilities of acoustic OAM applications.