Recent advances in experimental techniques allow one to create a quantum point contact between two Fermi superfluids in cold atomic gases with a tunable transmission coefficient. In this Rapid Communication we propose that three distinct behaviors of charge transports between two Fermi superfluids can be realized in this single setup, which are the multiple Andreev reflection, the self-trapping, and the Josephson oscillation. We investigate the dynamics of atom number difference between two reservoirs for different initial conditions and different transmission coefficients, and present a coherent picture of how the crossover between different regimes takes place. Our results can now be directly verified in the current experimental system.