Methods of forming dual core golf ball constructions achieving consistent and repeatable concentricity by incorporating a pair of novel partially cured hemispherical shells produced using an inventive center plate button. The pair of resulting novel hemispherical shells may be collectively compression molded about and reliably center a spherical inner core there within due to the novel resulting centering features/structure provided on the inner surface of each partially cured hemispherical shell by the novel center plate button used to form same. Securing features/structure are thereby provided within/on inner surfaces of resulting partially cured hemispherical shells in order to prevent undesirable movement of the spherical inner core there within until the final compression molding step occurs.