With a classical ensemble model that includes electron correlations during the whole ionization process, we investigate strong-field sequential double ionization of Ar by elliptically polarized pulses at the quantitative level. The experimentally observed intensity-dependent three-band or four-band structures in the ion momentum distributions are well reproduced with this classical model. More importantly, the experimentally measured ionization time of the second electrons by A. N. Pfeiffer et al. [Nature Phys. 7, 428 (2011)], which cannot be predicted by the standard independent-electron model, is quantitatively reproduced by this fully classical correlated model. The success of our work encourages classical descriptions and interpretations of the complex multielectron effects in strong-field ionization where nonperturbative quantum approaches are currently not feasible.