We conduct three-dimensional (3D) hydrodynamical simulations of common envelope evolution (CEE) of a neutron star (NS) that launches jets as it spirals in inside the envelope of a rotating red supergiant (RSG) stellar envelope and find that Rayleigh-Taylor instabilities form filamentary ejecta. We first study the 3D RSG envelope properties before we launch the jets. Adding envelope rotation causes the RSG envelope to expand in the equatorial plane and contract along the poles, leading to non-radial oscillations that decay after two oscillation periods, like the radial oscillation of the non-rotating model. In addition, the envelope becomes convective with large vortices, as in the non-rotating case. Since RSG stars oscillate and have envelope convection, we strengthen the claim that there is no need to relax one-dimensional stellar models of cool giant stars when transporting them to 3D grids. When adding jets, the 3D simulations that include pre-set envelope rotation show that envelope rotation leads to more prominent spiral structures of the ejecta than in the non-rotating case. We map the envelope zones that are Rayleigh-Taylor unstable and conclude that this instability forms the filamentary ejecta, with and without envelope rotation. The jet-inflated high-pressure volumes around the NS accelerate the envelope, a process prone to Rayleigh-Taylor instability.