Using a two-color plasma in air or gas allows for the generation of ultra-broadband and highly intense terahertz (THz) pulses. Precisely controlling the shape of THz pulses, particularly the carrier envelope phase, is crucial for a wide range of technological and scientific applications. Recent research has revealed that the phase difference between the fundamental laser wave and its second harmonic influences the shape of the emitted THz pulse. However, the combined impact of laser chirp and the air-dispersion-induced phase difference between the two colors has not been explored in detail. This study aims to fill this gap. The results show that both of these factors have a significant impact on the THz waveform and emitted pulse energy. Positive and negative chirps lead to distinct effects on the pulse shape. A positively chirped pump laser produces a THz waveform with a negative monopolar shape, while a negatively chirped pump laser results in a positive THz pulse shape. Additionally, our findings indicate that the relationship between THz pulse energy and chirp changes with variations in the specific phase difference between the first and second harmonics. These results underscore the importance of carefully tuning both parameters to achieve maximum generation efficiency for a given waveform.