This study systematically investigates the effect of laser powder bed fusion (LPBF) process parameters (hatch spacing: 40-120μm; scanning velocity: 800-1400 mm/s) on the relative density, microstructure and crystallographic texture of Ni51.47Ti48.33 (at.%) shape memory alloys. Furthermore, the mechanisms underlying the superelastic tension-compression asymmetry of LPBF NiTi alloys with <001>{100} cubic texture and <110>{001} Gross texture are elucidated. At hatch spacing of 40 and 80 μm, sufficient overlap between adjacent melt pools ensures densities exceeding 99.5% across the scanning velocity range. Melt pool morphology analysis reveals that the inheritance of grain orientations among melt pools facilitates texture formation, while scanning velocity modulates texture types by altering the angular deviations between grain-growth directions and thermal gradients. Superelasticity tests demonstrates that {100}-textured specimen exhibits superior recovery rate (97.1%) and cyclic stability, with exceptional recoverable strain (5.77%), but suffer dramatic reduction in tensile recoverable strain (1.24%). In contrast, {110}-textured specimen displays higher recoverable strain (4.12-4.5%) under both tension and compression, yet with significant irrecoverable strain (0.89~4.00%) and inferior cyclic stability. The tension-compression asymmetry originates from the strong orientation dependence of martensitic transformation characterized as unidirectional shear-mode as well as the differential activation tendencies of slip systems under varied loading orientations. This work establishes intrinsic relationships among LPBF parameters, texture evolution, and superelasticity, providing theoretical foundations for the regulation of LPBF NiTi alloys' superelasticity and design of multimodal actuator devices.