It will take some moments for the heated or cooled refrigerant to travel from the outdoor unit to the coil in the air handler, for the coil to adjust to the temperature change and begin to affect the passing air, and for the ducts to warm or cool from the passing air fully before you feel what you describe as the "effective temperature" at a supply register. "A few minutes" also describes the delay for air coming out of my registers supplying conditioned air from regular split AC units and natural gas furnaces.