Multi-agent pursuit-evasion tasks involving intelligent targets are notoriously challenging coordination problems. In this paper, we investigate new ways to learn such coordinated behaviors of unmanned aerial vehicles (UAVs) aimed at keeping track of multiple evasive targets. Within a Multi-Agent Reinforcement Learning (MARL) framework, we specifically propose a variant of the Multi-Agent Deep Deterministic Policy Gradient (MADDPG) method. Our approach addresses multi-target pursuit-evasion scenarios within non-stationary and unknown environments with random obstacles. In addition, given the critical role played by collective exploration in terms of detecting possible targets, we implement heterogeneous roles for the pursuers for enhanced exploratory actions balanced by exploitation (i.e. tracking) of previously identified targets. Our proposed role-based MADDPG algorithm is not only able to track multiple targets, but also is able to explore for possible targets by means of the proposed Voronoi-based rewarding policy. We implemented, tested and validated our approach in a simulation environment prior to deploying a real-world multi-robot system comprising of Crazyflie drones. Our results demonstrate that a multi-agent pursuit team has the ability to learn highly efficient coordinated control policies in terms of target tracking and exploration even when confronted with multiple fast evasive targets in complex environments.