We investigate the interfacial dynamics involved in the impact of a droplet on a liquid-liquid system, which involves the impingement of an immiscible core liquid drop from a vertical separation onto an interfacial shell liquid layer floating on a host liquid bath. The dynamics have been studied for a wide range of impact Weber numbers and two different interfacial shell liquids of varying volumes. The core drop, upon impact, dragged the interfacial liquid into the host liquid, forming an interfacial liquid column with an air cavity inside the host liquid bath. The dynamics is resolved into cavity expansion and rapid contraction, followed by thinning of the interfacial liquid. The interplay of viscous dissipation, interfacial pull, and core drop inertia influenced the necking dynamics. The viscous dissipation increases with the thickness of the interfacial layer, which depends on the volume and lateral spread over the water. The necking dynamics transitioned from inertia-dominated deep seal closure at higher spread, lower interfacial film volumes, and higher Weber numbers into inertia-capillary-dominated deep seal closure with an increase in film volumes, decrease in the spread of the interfacial fluid, or decrease in Weber number and finally into a no-seal closure at high volumes, low spread, and low Weber numbers.