Despite the advancements in high-performance computing and modern numerical algorithms, the cost remains prohibitive for multi-query kinetic plasma simulations. In this work, we develop data-driven reduced-order models (ROM) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation.Our ROM approach projects the equation onto a linear subspace defined by principal proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution into multiple time windows using a physical-time indicator and creating a temporally-local ROM.Applied to 1D--1V simulations, specifically the benchmark two-stream instability case, our time-windowed reduced-order model (TW--ROM) with the tensorial approach solves the equation approximately 450 times faster than Eulerian simulations while maintaining a maximum relative error of 3% for the training data and 12% for the testing data.