Software defined satellite-terrestrial networking has been identified as a promising approach to support the diversity of network services. As the fundamental issue to improve the flexibility of network management, the controller placement problem has been attracted increasing attentions for the integration of satellite and terrestrial networking. However, the impact of the dynamic coverage demands on the controller placement have not been well investigated in existed works, which makes them fail to adjust the coverage dynamically according to the actual demands, and leads to an obvious increase of networking response latency to the terminals. Aiming to address this issue, we propose a novel on-demand dynamic controller placement scheme, which can optimize the placement of controllers to improve networking response latency while meeting the dynamic coverage demands. Firstly, to optimize the number of controllers and meet the dynamic coverage demands, we define the coverage redundancy and propose the redundancy-based satellite subnet division method to establish the reliable satellite subnets. Secondly, we quantify the networking response latency of the distributed satellite subnet, and build an optimization mathematical model to optimize the number and location of controllers. Then, we formulate the controller placement problem into the capacitated facility location problem and build the mathematical model for it. Moreover, the on-demand dynamic approximation algorithm is proposed to obtain the approximation solution. Finally, the simulation results demonstrate that the proposed algorithm can effectively optimize the network latency compared with related algorithms.