Emitters showing thermally activated delayed fluorescence (TADF) in electroluminescent devices rely on efficient reverse intersystem crossing (rISC) arising from small thermal activation barriers between the lowest excited triplet and singlet manifolds. A small donor-acceptor compound consisting of a demethylacridine donor and a methylbenzoate acceptor group is used as a model TADF emitter. The spectroscopic signatures of this system are characterized using a combination of photoluminescence and photoluminescence excitation, and the photoluminescence decay dynamics are recorded between delays of 2 ns and 20 ms. Above T = 200 K, our data provide convincing evidence for TADF at intermediate delays in the microsecond range, whereas triplet-triplet annihilation and slow triplet decay at later times can be observed over the entire temperature range from T = 80 K to room temperature. Moreover, close to room temperature, we find a second and faster up-conversion mechanism, tentatively assigned to reverse internal conversion between different triplet configurations. An interpretation of these experimental findings requires a calculation of the deformation patterns and potential minima of several electronic configurations. This task is performed with a range-separated hybrid functional, outperforming standard density functionals or global hybrids. In particular, the systematic underestimation of the energy of charge transfer (CT) states with respect to local excitations within the constituting chromophores is replaced by more reliable transition energies for both kinds of excitations. Hence, several absorption and emission features can be assigned unambiguously, and the observed activation barriers for rISC and reverse internal conversion correspond to calculated energy differences between the potential surfaces in different electronic configurations.