This work reveals essential details of plasma-surface interaction in atmospheric air that are important for a wide range of applications, beginning from airflow control and up to the high-voltage insulation. The paper discusses experimental data characterizing dynamics of development and kinetics of energy coupling in surface dielectric barrier discharge (SDBD), atmospheric air plasmas sustained over dielectric surfaces, over a wide range of time scales. The experiments have been conducted using microsecond pulse voltage waveform of single and alternating polarities. Time-resolved discharge development and mechanisms of coupling with quiescent air are analyzed using nanosecond gate camera imaging, electrical measurements, and original surface charge sensors. The results demonstrate several new, critically important processes overlooked in previous studies. Specifically, it is shown that SDBD plasmas energy release may be significantly increased by using an optimized waveform.