coupling, respectively. These classical Gaussian noises are partially correlated. The transient evolution of qubit is studied for the regimes: (a) the interwell incoherent tunneling, (b) the relaxation of interlevel population, and (c) the decoherence of the off-diagonal part of a density matrix. For all regimes, the relaxation rates and the frequency renormalization [for the case (c)] are analyzed versus the parameters of qubit and couplings to the noises applied through different channels. The fluctuation effect restricts an averaged description of evolution processes, so that the dissipative dynamics is not valid at tails of relaxation. The results obtained open a way for verification of relaxation parameters and demonstrate a possibility for minimization of coupling between qubit and environment. Under typical level of noises, the contributions considered here are comparable to recent experimental data on the population relaxation and the interwell tunneling.