The dissipative Kerr solitons offer broadband coherent and low-noise frequency combs and stable temporal pulse trains, having shown great potential applications in spectroscopy, communications, and metrology. Here, we have demonstrated the dissipative Kerr soliton generation in a microrod resonator and silicon nitride (Si₃N₄) microrings, by utilizing an auxiliary-laser assisted thermal response control. We have studied the evolution of the soliton generation processes during the scanning of the pump laser detuning, especially the breathing dissipative Kerr soliton, which shows uncertainties of around megahertz (MHz) order of the breathing period. This instability is the main obstacle for future applications. By applying a modulated signal to the pump laser, the breathing frequency can be injection locked to the modulation frequency and tuned over tens of MHz with frequency noise significantly suppressed. Our demonstration offers an alternative knob for the control of soliton dynamics in microresonators and paves a new avenue towards practical applications of breathing solitons.