This study introduces a distributed specified-time control mechanism (DSTCM) for secondary control in islanded microgrids (MGs) operating under directed switching communication topologies. The proposed mechanism ensures convergence properties that are independent of initial conditions, enabling the design of an exact offline settling time to reduce power losses and limit the upper bound of convergence time. By employing a piecewise function-based communication approach and directed switching graphs, the proposed mechanism effectively reduces computational and communication demands on the system. Moreover, the proposed mechanism significantly enhances power system performance while minimizing adjustment costs, delivering precise control actions under various operating conditions. The accuracy and effectiveness of the proposed mechanism are validated through extensive MATLAB simulations, demonstrating its ability to regulate MG voltages and frequencies, achieve accurate proportional active power sharing, and maintain state-of-charge (SoC) balancing. Its superiority over previously established mechanisms is also confirmed by a comparative analysis.