The oscillation instability of sessile drops is ubiquitous in surface acoustic wave (SAW) -powered digital microfluidics. Yet the physics underlying these phenomena has not been elucidated owing to the complex interplay between hydrodynamics, acoustics, and capillarity. We decipher the instability by combining high-speed imaging of the droplet surface vibration with inner acoustic pressure measurements. We rationalize the observed behavior with a model inspired from optomechanics, which couples an intracavity acoustic mode excited by the SAW to a surface deformation eigenmode through amplitude modulation and delayed radiation pressure feedback