We have developed an evolutionary turbulent model of the Jovian subnebula consistent with the extended core accretion formation model of Jupiter. This model takes into account the vertical structure of the subnebula, as well as the evolution of the surface density as given by an α-disk model and is used to calculate the thermodynamical conditions in the subdisk for different values of the viscosity parameter. We show that the Jovian subnebula evolves in two different phases during its lifetime. In the first phase, the subnebula is fed through its outer edge by the solar nebula as long as it has not been dissipated. In the second phase, the solar nebula has disappeared and the Jovian subdisk expands and gradually clears with time as Jupiter accretes the remaining material. We also demonstrate that early generations of satellites formed during the beginning of the first phase of the subnebula cannot survive in this environment and fall onto the proto-Jupiter. As a result, these bodies may contribute to the enrichment of Jupiter in heavy elements. Moreover, migration calculations in the Jovian subnebula allow us to follow the evolution of the ices/rock ratios in the proto-satellites as a function of their migration pathways. By tempting to reproduce the distance distribution of the Galilean satellites, as well as their ices/rock ratios, we obtain some constraints on the viscosity parameter of the Jovian subnebula.