The time evolution of a correlated multi-electron state in a semiconductor coupled quantum dot, interacting with the acoustic phonon bath, is calculated within the master equation formalism, including electron-electron interaction exactly through the configuration-interaction approach. The system is evolved after an initialization phase, with the system under strong bias, leading to the charge density mainly localized in one of the dots. When the system is evolved (in unbiased condition), damped multi-frequency charge oscillations are found, which strongly depend on the 3D system geometry and initialization. We describe the approach used to obtain the multi-electron states and to include the phonon-induced transitions between them in the time evolution. Furthermore, the effect of a magnetic field applied in the axial direction of the vertical double-dot cylindrical structure is discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)