We assess the Pacific Tsunami Warning Center’s (PTWC) capabilities as the local tsunami warning center for Puerto Rico and the Virgin Islands (PRVI), relying on the computation of theoretically optimum detection and response times. We computed theoretical P‐ and S‐wave detection times for both the Caribbean and a subregion encompassing PRVI. In these computations, we considered not only the topology of the seismic network, but also the data latency of its stations. To account for both factors as realistically as possible, we used a snapshot of the latencies of the data streams coming into the PTWC system on 29 August 2017. The resulting maps show a significant reduction of the area where we could detect earthquakes within 60 s in the Caribbean region from 28% to 6.6% of the total area. Likewise, in the eastern Caribbean, both station outages and long data latencies at 68% of the seismic network nullify the potential gains in response time otherwise possible by taking advantage of the shortest detection times in areas with the highest density of stations, such as the island of Puerto Rico. Notwithstanding, faster release of automatic solutions combined with the reduction of data latencies can shorten tsunami bulletin release times by about one minute, albeit with fewer magnitude computations. In the future, the PTWC hopes to release most events in the densely instrumented parts of the eastern Caribbean within two minutes of origin time.