An implementation of real-time time-dependent Hartree-Fock (RT-TDHF) and current density functional theory (RT-TDCDFT) for molecules in strong uniform magnetic fields is presented. In contrast to earlier implementations, the present work enables the use of the RT-TDCDFT formalism, which explicitly includes field-dependent terms in the exchange-correlation functional. A range of current-dependent exchange-correlation functionals based on the TPSS functional are considered, including a range-separated variant, which is particularly suitable for application to excited state calculations. The performance of a wide range of propagator algorithms for real-time methods is investigated in this context. A recently proposed molecular orbital pair decomposition analysis allows for assignment of electronic transitions, providing detailed information about which molecular orbitals are involved in each excitation. The application of these methods is demonstrated for the electronic absorption spectra of N2 and H2O both in the absence and in the presence of a magnetic field. The dependence of electronic spectra on the magnetic field strength and its orientation relative to the molecule is studied. The complex evolution of the absorption spectra with magnetic field is rationalized using the molecular orbital pair decomposition analysis, which provides crucial insight in strong fields where the spectra are radically different from their zero-field counterparts.