Most surfaces treated by atmospheric pressure plasma jets (APPJs) in practical applications are notably three-dimensional. However, non-planar surfaces exhibit a diverse array of geometries, such as variations in curvature, roughness, and texture, complicating the prediction of surface ionization waves (SIW) propagation behavior across varied surface shapes, in the absence of sufficient experimental data. In this study, we made measurements of APPJ interactions with the non-planar substrates using the spatio-temporal resolved image method. Non-planar substrates encompassed wavy surfaces, arrayed hemispheres, and randomly textured raised surfaces. We tracked the morphology and velocity of SIW propagation over these surfaces. The results indicate that the SIW propagation on non-planar surfaces is significantly influenced by surface geometry and displays path selectivity, i.e., the SIW tends to propagate along valleys. The average propagation velocity of the SIW increases with the increasing radius of the wavy surface, as well as with the increased height of the arrayed hemispheres. This is attributable to the surface geometry constraining the dispersion of the SIW, causing it to concentrate and propagate in a singular direction. Moreover, the surface geometry markedly affects the distribution of the plasma treatment area, with the plasma inclined to enter valleys (where the light emission is significantly stronger than that of peaks) and to closely adhere to hemispherical surfaces. These patterns suggest a potential positive impact on treating skin surfaces such as pores, reducing bacteria in wrinkles, and addressing pimples.