The laser-induced spin dynamics of FeCo in perpendicularly magnetized L10-MnGa/FeCo bilayers with ferromagnetic and antiferromagnetic interfacial exchange coupling (IEC) are examined using the time-resolved magneto-optical Kerr effect. We found a precessional phase reversal of the FeCo layer as the IEC changes from ferromagnetic to antiferromagnetic. Moreover, a precession-suspension window was observed when the magnetic field was applied in a certain direction for the bilayer with ferromagnetic IEC. Our observations reveal that the spin dynamics modulation is strongly dependent on the IEC type within the Landau-Lifshitz-Gilbert depiction. The IEC dependence of the precessional phase and amplitude suggests the interesting method for magnetization dynamics modulation.