Silver clusters grown in helium nanodroplets are excited by intense femtosecond laser pulses resulting in the formation of a hot electron plasma far from equilibrium. The ultrafast dynamics is studied by applying optically delayed dual pulses, which allows us to pursue and control the coupling of the laser field to the clusters on a femtosecond time scale. A distinct influence of the optical delay on the ionization efficiency gives strong evidence that a significant contribution of collective dipolar electron motion is present, which is verified by corresponding Vlasov dynamics simulations on a model system. The microscopic approach demonstrates the outstanding role of giant resonances in clusters also in intense laser fields.