The time evolution of the mean values (centroids) and the variances (widths) in the fission process of is studied by using an analytically solvable quantum mechanical model of coupled oscillators in collective coordinates of charge and mass asymmetries. Our model is based on a non-perturbative formalism. It is found that in the exchange process during fission the charge and mass motions become correlated rather fast. The shell effects in potential energy surfaces are shown to have very little effect on the time evolution process of both the mean values and variances.