We revisit the excitation-tunneling process in nonsequential double ionization (NSDI) of helium in an 800-nm laser field. The correlated two-electron momentum distributions are calculated by using the improved quantitative rescattering (QRS) model, in which the lowering of the threshold energy due to the presence of an electric field at the instant of recollision is taken into account. In the framework of the QRS model, the correlated two-electron momentum distributions for excitation-tunneling in NSDI can be factorized as a product of the returning-electron wave packet (RWP) and the field-free differential cross section (DCS) for electron impact excitation of the parent ion multiplied by the tunneling ionization rate of electrons in the excited states. The RWPs, which describe the momentum distribution of the returning electrons, are obtained within the strong-field approximation for high-order above-threshold ionization. The DCSs for electron impact excitation of He+ are calculated using the state-of-the-art many-electron R-matrix theory, and the tunneling ionization rates for electrons in the excited states are evaluated by solving the time-dependent Schrödinger equation. The calculated correlated two-electron momentum distribution shows that the fourfold symmetry with regard to the parallel momentum components is broken. This is in contradiction to the prevalent view that the correlation pattern for excitation-tunneling in NSDI is symmetric with respect to the coordinate axes. By including the recollisional (e,2e) process, the predicted correlated two-electron momentum distributions are found to be in good qualitative agreement with experiment.