Exotic nuclei are characterized by having a number of neutrons (or protons) in excess relative to stable nuclei. Their shell structure, which represents single-particle motion in a nucleus(1,2), may vary due to nuclear force and excess neutrons(3-6), in a phenomenon called shell evolution(7). This effect could be counterbalanced by collective modes causing deformations of the nuclear surfaces(8). Here, we study the interplay between shell evolution and shape deformation by focusing on the magnetic moment of an isomeric state of the neutron-rich nucleus Cu-75. We measure the magnetic moment using highly spin-controlled rare-isotope beams and achieve large spin alignment via a two-step reaction schemes(9) that incorporates an angular-momentum-selecting nucleon removal. By combining our experiments with numerical simulations of many-fermion correlations, we find that the low-lying states in Cu-75 are, to a large extent, of single-particle nature on top of a correlated Ni-74 core. We elucidate the crucial role of shell evolution even in the presence of the collective mode, and within the same framework we consider whether and how the double magicity of the Ni-78 nucleus is restored, which is also of keen interest from the perspective of nucleosynthesis in explosive stellar processes.