This work focuses on the propagation dynamics of the Fisher-KPP equation featuring spatial nonlocal diffusion. In contrast to classical local diffusion, where the propagation shape is solely determined by the diffusion matrix, and the reaction rate merely scales its size without altering its geometry, the core objective is to reveal how, under nonlocal diffusion, the nonlinear reaction rate fundamentally sculpts and transforms the asymptotic invasion shape of the propagating front.