Magnetic skyrmions are nanosized topological spin textures stabilized by a delicate balance of magnetic energy terms. The chemical substitution of the underlying crystal structure of skyrmion-hosting materials offers a route to manipulate these energy contributions but also introduces additional effects such as disorder and pinning. While the effects of doping and disorder have been well studied in B₂0 metallic materials such as Fe_1−xCo_xSi and Mn_1−xFe_xSi, the consequences of chemical substitution in the magnetoelectric insulator Cu₂OSeO₃ have not been fully explored. In this work we utilize a combination of AC magnetometry and small-angle neutron scattering to investigate the magnetic phase transition dynamics in pristine and Zn-substituted Cu₂OSeO₃. The results demonstrate that the first-order helical-conical phase transition exhibits two thermally separated behavioral regimes: at high temperatures, the helical and conical domains transform by large-scale, continuous rotations, while at low temperatures, the two phases coexist. Remarkably, the effects of pinning in the substituted sample are less prevalent at low temperatures compared to high temperatures, despite the reduction of available thermal activation energy. We attribute this behavior to the large, temperature-dependent, cubic anisotropy unique to Cu₂OSeO₃, which becomes strong enough to overcome the pinning energy at low temperatures. Consideration and further exploration of these effects will be crucial when engineering skyrmion materials towards future applications.