The classical Jeans instability framework provides a conceptual foundation for understanding self-gravitational collapse and subsequent star formation in interstellar environments. However, cosmic plasmas are inherently magnetized and frequently collisionless, exhibiting significant departures from local thermodynamic equilibrium. While linear theories predict initial instability thresholds, they fail to track the long-term nonlinear runaway dynamics. We present a fluid simulation investigating the nonlinear evolution of the Jeans instability in a magnetized tricomponent complex (dusty) plasma. The constituent nonthermal electrons and ions are governed by the κ-distribution law, while the heavier dust grains are treated in a fluid framework, coupled with a uniform ambient magnetic field. The numerical architecture utilizes a fourth-order finite difference method (FDM) for spatial gradients and a second-order leap-frog time-integration scheme. We systematically investigate the complex interplay among the self-gravitational attraction, nonthermal electrostatic screening, and magnetic pressure across a wide range of magnetic field strengths and degrees of nonthermality. It is found that enhanced nonthermality accelerates structural localization, while the magnetic field introduces a critical pressure barrier that suppresses the instability. In highly magnetized environments, thermal and nonthermal systems exhibit identical growth rate characteristics, indicating that magnetic pressure dominates the nonthermal thermostatistics in the strong magnetic regime. This study develops a comprehensive and numerically robust framework to understand early-stage star formation and evolution processes in nonthermal astrophysical media.