Physisorption on hexagonal boron nitride (hBN) gained interest over the years thanks to its properties (chemically and thermally stable, insulating properties, etc.) and similarities to the well-known graphene. A recent study showed flat-on adsorption of several cationic thiacarbocyanine dyes on hBN with a tendency to form weakly coupled H- or I-type aggregates, while a zwitterionic thiacarbocyanine dye rather led to a tilted adsorption. With this in-depth time-resolved study using the TC-SPC technique, we confirm the results proven by adsorption isotherms, atomic force microscopy, and stationary state spectroscopy combined with molecular mechanics simulations and estimation of the corresponding exciton interaction. The absence of a systematic trend for the dependence of the decay times, normalized amplitudes of the decay components, and contribution of different components to the stationary emission spectra upon the emission wavelength observed for all studied dyes and coverages suggests the occurrence of a single emitting species. At low coverage levels, the non-mono-exponential character of the decays was attributed to adsorption on different sites characterized by different intramolecular rotational freedom or energy transfer to nonfluorescent traps or a combination of both. The difference between the decay rates of the four dyes reflects a different density of the nonfluorescent traps. Although the decay time of the unquenched dyes was in the order of magnitude of that of dye monomers in a rigid environment, it is also compatible with weakly coupled aggregates such as proposed earlier based on the stationary spectra. Hence, the adsorption leads to a rigid environment of the dyes, blocking internal conversion. Increasing the concentration of the dye solution from which the adsorption on hBN occurs increases not only the coverage of the hBN surface but also the extent of energy transfer to nonfluorescent traps. For TDC (5,5-dichloro-3-3′-diethyl-9-ethyl-thiacarbocyanine) and TD2 (3-3′-diethyl-9-ethyl-thiacarbocyanine), besides direct energy transfer to traps, exciton hopping between dye dimers followed by energy transfer to these traps occurs, which resulted in a decreasing decay time of the longest decaying component. For all dyes, it was also possible to analyze the fluorescence decays as a stretched exponential as would be expected for energy transfer to randomly distributed traps in a two-dimensional (2D) geometry. This analysis yielded a fluorescence decay time of the unquenched dyes similar to the longest decay time obtained by analysis of the fluorescence decays as a sum of three of four exponentials.