We numerically investigate the excitation of vector solitonic pulse with orthogonally polarized components via free-carrier effects in microresonators with normal group velocity dispersion (GVD). The dynamics of single, dual and oscillated vector pulses are unveiled under turn-key excitation with a single frequency-fixed CW laser source. Parameter spaces associated with detuning, polarization angle, interval between the pumped orthogonal resonances and pump amplitude have been revealed. Different vector pulse states can also be observed exploiting the traditional pump scanning scheme. Simultaneous and independent excitation regimes are identified due to varying interval of the orthogonal pump modes. The nonlinear coupling between two modes contributes to the distortion of the vector pulses’ profile. The free-carrier effects and the pump polarization angle provide additional degrees of freedom for efficiently controlling the properties of the vector solitonic microcombs. Moreover, the crucial thermal dynamics in microcavities is discussed and weak thermal effects are found to be favorable for delayed vector pulse formation. These findings reveal complex excitation mechanism of solitonic structures and could provide novel routes for microcomb generation. © 2023 OSA - The Optical Society. All rights reserved.