Cylindrical ferromagnetic tubes are notable for their geometry-driven physical phenomena, making them promising for future technological applications. Self-assembly rolling technology is used to create tubes with high surface quality and side edges, which are crucial for customizing magnetic anisotropy through magnetostatic interactions at the edges. This study investigates the anisotropy induced by these interactions in magnetostriction-free permalloy membranes. Thin planar membranes of varying dimensions were transformed into tubular structures with curvature radii in the tens of microns and winding numbers from 0.6 to 1.5. Experimental results reveal that magnetostatic energy is minimized when the winding number exceeds 0.8-0.9 by adopting an azimuthal domain pattern, or flux-closure configuration, from previously axial domains. These results are supported by analytical calculations of the equilibrium magnetic state of both planar and curved membranes, considering shape anisotropy constants. These constants were derived from magnetostatic energy calculations assuming a single domain configuration and applied to various geometries and curvatures. This research advances the understanding of anisotropy tuning in curved thin-film architectures, focusing on achieving azimuthal magnetic anisotropy in soft ferromagnetic tubular structures without additional induced anisotropy, a key step for applications in data storage, field sensors, and biomedicine relying on 3D magnetic structures.