This work presents an extension of the online-adaptive hyperreduced reduced basis (RB) element method for parametrized nonlinear component-based systems [1] to time-dependent problems. Standard reduced basis methods face challenges with topology-varying configurations and high-dimensional parameter spaces due to the prohibitive cost of global offline training. To address these challenges, we utilize a component-based framework that decomposes global domains into smaller, computationally manageable subdomains selected from a library of interoperable archetype components. The primary contribution of this research is the introduction of a spatio-temporal online-adaptive refinement strategy for both RB and hyperreduction fidelities. In the offline phase, we construct a library of archetype components equipped with multi-fidelity RB spaces and corresponding reduced quadrature rules [2]. In the online phase, we employ a hierarchical error estimation framework that compares solutions at successive fidelity levels to drive the adaptation. Unlike previous steady-state formulations, the proposed method adaptively selects the optimal fidelity for each component and port at each time step. This ensures that the user-prescribed system-level error tolerance is met efficiently by only enriching the RB and hyperreduction fidelities in spatial regions and time intervals where the local error indicators are highest. The effectiveness of the method is demonstrated on two-dimensional hyperelastic systems. Numerical results indicate that (i) the hyperreduced reduced RB method provides O(100) speedup relative to the full-order model and (ii) the adaptive spatio-temporal enrichment provides significant computational savings compared to uniformly refined reduced-order models by selectively targeting transient features and localized stress concentrations. REFERENCES [1] M. Ebrahimi and M. Yano. An online-adaptive hyperreduced reduced basis element method for parameterized component-based nonlinear systems using hierarchical error estimation. Computer Methods in Applied Mechanics and Engineering, Vol. 449, pp.118590, 2026. [2] M. Yano and A.T. Patera. An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs. Computer Methods in Applied Mechanics and Engineering, Vol. 344, pp.1104-1123, 2019.