Transition metal dichalcogenides (TMDs) are nanostructured semiconductors with prospects in optoelectronics and photocatalysis. Several bottom-up procedures to synthesize such materials have been developed yielding colloidal transition metal dichalcogenides (c-TMDs). Where such methods initially yielded multilayered sheets with indirect band gaps, recently, also the formation of monolayered c-TMDs became possible. Despite these advances, no clear picture on the charge carrier dynamics in monolayer c-TMDs exists to date. Here, we show through broadband and multiresonant pump-probe spectroscopy, that the carrier dynamics in monolayer c-TMDs are dominated by a fast electron trapping mechanism, universal to both MoS2 and MoSe2, contrasting hole-dominated trapping in their multilayered counterparts. Through a detailed hyperspectral fitting procedure, sizable exciton red shifts are found and assigned to static shifts originating from both interactions with the trapped electron population and lattice heating. Our results pave the way to optimizing monolayer c-TMDs via passivation of predominantly the electron-trap sites.