Context. Low- and intermediate-mass asymptotic giant stars and massive red supergiant stars are important contributors to the chemical enrichment of the Universe. They are among the most efficient dust factories of the Galaxy, harboring chemically rich circumstellar environments. Yet, the processes that lead to dust formation or the large-scale shaping of the mass loss still escape attempts at modeling. Aims. Through the ATOMIUM project, we aim to present a consistent view of a sample of 17 nearby cool evolved stars. Our goals are to unveil the dust-nucleation sites and morphologies of the circumstellar envelope of such stars and to probe ambient environments with various conditions. This will further enhance our understanding of the roles of stellar convection and pulsations, and that of companions in shaping the dusty circumstellar medium. Methods. Here we present and analyze VLT/SPHERE-ZIMPOL polarimetric maps obtained in the visible (645–820 nm) of 14 out of the 17 ATOMIUM sources. They were obtained contemporaneously with the ALMA high spatial resolution data. To help interpret the polarized signal, we produced synthetic maps of light scattering by dust, through 3D radiative transfer simulations with the RADMC3D code. Results. The degree of linear polarization (DoLP) observed by ZIMPOL spreads across several optical filters. We infer that it primarily probes dust located just outside of the point spread function of the central source, and in or near the plane of the sky. The polarized signal is mainly produced by structures with a total optical depth close to unity in the line of sight, and it represents only a fraction of the total circumstellar dust. The maximum DoLP ranges from 0.03–0.38 depending on the source, fractions that can be reproduced by our 3D pilot models for grains composed of olivine, melilite, corundum, enstatite, or forsterite. The spatial structure of the DoLP shows a diverse set of shapes, including clumps, arcs, and full envelopes. Only for three sources do we note a correlation between the ALMA CO υ = 0, J = 2−1 and SiO υ = 0, J = 5−4 lines, which trace the gas density, and the DoLP, which traces the dust. Conclusions. The clumpiness of the DoLP and the lack of a consistent correlation between the gas and the dust location show that, in the inner environment, dust formation occurs at very specific sites. This has potential consequences for the derived mass-loss rates and dust-to-gas ratio in the inner region of the circumstellar environment. Except for π¹ Gru and perhaps GY Aql, we do not detect interactions between the circumstellar wind and the hypothesized companions that shape the wind at larger scales. This suggests that the orbits of any other companions are tilted out of the plane of the sky.