The interaction of dielectric barrier discharge plasma and silicone-oil liquid droplet in a Hele-Shaw cell was investigated experimentally employing synchronized optical and electrical time-resolved measurements. Temporal development of the destabilization, stretching, and fragmentation of the plasma-liquid interface was studied for the whole event lifespan. The perturbation wavelength and temporal development of fingering speed, plasma-liquid interface length, mean transferred charge, and fractal dimension of the pattern were determined. Recorded changes in the dissipated mean power show a strong correlation to subsequent stretching of the interface, opening new methodological possibilities for future investigations. Our extensive parametric study shows that oil viscosity and applied voltage amplitude both have a significant impact on the interface evolution. Notably, at relatively high voltages the destabilized interface featured properties noticeably diverging from the theoretical prediction of a known model. We propose an explanation based on the change of the liquid viscosity with increased heating at high applied voltage amplitudes.