We present a method for real-time propagation of electronic wave functions, within time-dependent density functional theory (RT-TDDFT), coupled to ionic motion through mean-field classical dynamics. The goal of our method is to treat large systems and complex processes, in particular photocatalytic reactions and electron transfer events on surfaces and thin films. Due to the complexity of these processes, computational approaches are needed to provide insight into the underlying physical mechanisms and are therefore crucial for the rational design of new materials. Because of the short time step required for electron propagation (of order similar to 10 attoseconds), these simulations are computationally very demanding. Our methodology is based on numerical atomic-orbital-basis sets for computational efficiency. In the computational package, to which we refer as TDAP-2.0 (Time-evolving Deterministic Atom Propagator), we have implemented a number of important features and analysis tools for more accurate and efficient treatment of large, complex systems and time scales that reach into a fraction of a picosecond. We showcase the capabilities of our method using four different examples: (i) photodissociation into radicals of opposite spin, (ii) hydrogen adsorption on aluminum surfaces, (iii) optical absorption of spin-polarized organic molecule containing a metal ion, and (iv) electron transfer in a prototypical dye sensitized solar cell.