Powerful, broadband terahertz (THz) pulses and its application attract an exponential growth of interests. Dual-color laser filamentation in gases is one of the promising THz sources because of the scalability of the THz energy and wavelength with input parameters. But the additional phase induced by the nonlinearities associated with high intensities cannot be neglected because it may result in modulation of the THz waves. We investigate the influences of the infrared pump energy and air dispersion on the terahertz generation in dual-color laser filament. We observe that optimum dual-color laser relative phase of the THz generation undergoes a linear shift with increasing pump energy due to the intensity-induced refractive index change. This phase shift is verified by the spectral broadening of a two-color laser affected by the same mechanism. The result improves our understanding of the theoretical framework for a higher power THz source.