Direct current (DC) transmission is highly regarded for its ability to dynamically decouple AC power systems by segmenting them into disjoint networks. Such configurations lead to more efficient power transfers and better oscillation damping, but necessitate controllers with seemingly heavy communication requirements that rely on wide-area measurement systems. This paper shows that DC-segmented power systems are poset-causal, making them amenable to powerful decentralized control techniques that can substantially reduce their communication needs. Specifically, optimal decentralized control is attainable with communication only between AC subsystems that are directly connected by a DC line. The approach explicitly leverages the implied graph structure of power systems with AC and DC lines. Numerical results demonstrate that the decentralized controller achieves nearly the same performance as the optimal centralized controller.