We study the spreading characteristics of a reactive-wetting system of mercury (Hg) droplets on silver (Ag) films in room temperature. This is done using our recently developed method for reconstructing the dynamical three-dimensional shape of spreading droplets from two-dimensional microscope images. We study the time evolution of the droplet radius and its contact angle, and find that the spreading process consists of two stages: (i) the "bulk propagation" regime, controlled by chemical reaction on the surface, and (ii) the "fast-flow" regime, which occurs within the metal film as well as on the surface and consists of both reactive and diffusive propagation. We show that the transition time between the two main time regimes depends solely on the thickness of the Ag film. We also discuss the chemical structure of the intermetallic compound formed in this process.