A general theory is presented describing the photo-excitation dynamics of transient, paramagnetic triplet states of aromatic molecules including their absorption properties in a molecular host crystal when irradiated by a pulsed laser beam. It is applied to the system of a pentacene doped naphthalene single crystal, where the photo-excitation of pentacene results in a highly non-equilibrium population of intermediate electronic triplet states. These paramagnetic states can be addressed to align the proton spins of the naphthalene host at moderate experimental conditions using dynamic nuclear polarisation (DNP). The photo-excitation profile and the resulting triplet state distribution, which is determined by the material and the laser parameters, leads to a corresponding proton polarisation profile. Measurements of the resulting polarisation inhomogeneity by spatially resolved neutron transmission confirm the theory. The theoretical model then allows the extraction of crucial parameters that enable quantitative investigations of the dynamics of spin systems. For applications of triplet DNP with pentacene-doped naphthalene crystals, polarisation maximum, homogeneity and build-up rate are key factors, and the theory allows the identification of optimal experimental parameters depending on the priorities placed on these factors.