The service used in AEM to control how AEM instances interact with a topology while running on instances is the Apache Sling Resource-Based service. This service helps in managing the resources and how they're resolved and accessed within the AEM topology. It's part of the Apache Sling framework, which is an integral part of AEM's architecture.
Option A, "Web Console Service," is more for administration and management of OSGi components, not specifically for topology interaction.
Option C, "Offloading Service," is generally related to processing tasks outside of the AEM instances and does not directly control instance interactions within a topology.