Time-to-Live (TTL) caches decouple the occupancy of objects in cache through object-specific validity timers. Stateof- the art techniques provide exact methods for the calculation of object-specific hit probabilities given entire cache hierarchies with random inter-cache network delays. The system hit probability is a provider-centric metric as it relates to the origin offload, i.e., the decrease in the number of requests that are served by the content origin server. In this paper we consider a user-centric metric, i.e., the response time, which is shown to be structurally different from the system hit probability. Equipped with the state-of-theart exact modeling technique using Markov-arrival processes we derive expressions for the expected object response time and pave a way for its optimization under network delays.