With the advances in ultra-strong and ultra-short laser pulses, many research works have concentrated on the real-time control of molecular dynamics. Apart from plotting the wave packet dynamics data of the electronic state, the state population is also capable of reflecting the excitation, dissociation and ionization of molecules. By controlling the wave packet evolution, the state population can be manipulated, thereby facilitating the optical control over the molecular processes experimentally. NaI molecule is a reference molecule for monitoring wave packet evolution experimentally and theoretically because a crossing is present between two electronic states that are coupled in a nonadiabatic way. The wave packet moves periodically between the internal and external turning points, which induced the periodical change of the photoelectron spectrum. Many researches mainly investigated the photoelectron spectrum, the competitive ionization channel and the predissociation dynamics of the first passage through the crossing region. Although the photoelectron spectrum offers the significant plotting of the exited-state movement of wave packets and ionization yields, it is not enough to reflect the excitation, dissociation as well as ionization processes of molecules. Herein, this work focuses on the study of the respective parameter effects of pump and probe pulses on the probabilities of excitation and ionization, and the total probability of dissociation of NaI molecules, which are examined completely and quantitatively analyzed. State populations of the ground and excited states of NaI and the ionic ground state of NaI⁺ are calculated by adopting a time-dependent wave packet method, because it has the intuition of classical mechanics, no lack of accuracy of quantum mechanics. By appropriately changing the laser parameters, the population on each state can be controlled, and so can the excitation, dissociation and ionization probabilities. The dissociation increases while the ionization decreases when the delay time is prolonged. The pump-probe delay time evolution of total dissociation probability reveals a series of increasing stair-stepped plateaus, which are indicative of the individual parts of the wave packet reaching the asymptotic region i.e., discontinuous dissociation process. The results reveal an increase in the excitation, marginal decrease in dissociation probability, and marginal increase in ionization probability with increasing pump laser intensities.With the increase in pump wavelength, the excited state population increases initially and then decreases, reflecting the resonant region of 313~328 nm. The ionization probability increases while the dissociation probability decreases with the increase of the pump wavelength. The dissociation probability associates with the wave packet propagation velocity and the time taken for passing through the crossing zone. A pulse with a shorter wavelength indicating the higher energy, causes a wave packet with a higher velocity at the crossing point, increasing the predissociation. The dissociation probability decreases slightly with enhancing pump pulse width for shorter pulse widths, in which the propagation velocity dominates. The dissociation probability increases slightly with rising pump pulse width for longer pulse widths, in which the propagation time dominates. As suggested by the derived results, pump laser is the sole influencing factor of molecular excitation and dissociation, while the ionization was affected by both pump and probe lasers. The seemingly counterintuitive understanding: the pump pulse affects the ionization probability, can be clarified. The pump laser parameters affect the dissociation of the wave packets moving between the internal and external points before the probe pulse appears. Then ionization may occur when the probe pulse appears at 3 000 fs. The ionization follows the general understanding of photoionization: ionization occurs when the photon energy is greater than the ionization energy, and the ionization probability is determined by the ionization dipole moment at the internuclear distance for the delay time of 3 000 fs. In other words, The dissociation and ionization processes compete and coexist, the pump pulse affects the wave packets before ionization through affecting the dissociation, thus affects the ionization. This provides an additional control means for controlling ionization, and even a very effective way. The laser field with weak field intensity, short wavelength, narrow pulse width and long delay time is conducive to dissociation, on the contrary, it is conducive to ionization. The control of the excitation, dissociation, and ionization yields can be possible by adjusting the form of the laser pulse. The obtained findings are crucially valuable for the molecular spectroscopy, which can also contribute to attain optical molecular control experimentally.