When I turn my thermostat on at first I hear a humming then it blows hot air then cold air. I was told I need an Inducer motor? Does that sound correct?

Likely it is the hot air in the Ductwork, then the cooled air, heat works when voltage from thermostat wire(white?) goes back to heat relay/contactor, If it is a "Modern" control board, it could introduce additional problems.
Like to hear other advice, couple of good people here.