Island microgrids play a crucial role in developing and utilizing offshore renewable energy sources. However, high operation costs and limited operational flexibility are significant challenges. To address these problems, this paper proposes a novel dual−layer distributed optimal operation methodology for islanded microgrids. The lower layer is a distributed control layer that manages multiple controllable distributed fuel−based microturbines (MTs) within the island microgrids. A novel adaptive consensus control method is proposed in this layer to ensure uniform operating status for each MT. Moreover, the proposed method can achieve the total output power of MTs to follow the reference signal provided by the upper layer while ensuring plug−and−play capability for MTs. The upper layer is an optimal scheduling layer that manages various forms of controllable distributed power sources and provides control reference signals for the lower layer. Additionally, a two−stage twin−delayed deterministic policy gradient (MATD3) algorithm is utilized in this layer to minimize the operating costs of island microgrids while ensuring their safe operation. Simulation results demonstrate that the proposed methodology can effectively reduce the operating costs of island microgrids, unify the operational status of MTs, and achieve plug−and−play capability for MTs.