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A spatially and temporally heterogeneous environment may lead to unexpected population dynamics. Knowledge still is needed on which of the local environment properties favour population maintenance at larger scale. For pathogen vectors, such as tsetse flies transmitting human and animal African trypanosomosis, such a knowledge is crucial to design relevant management strategies. We developed an original mechanistic spatio-temporal model of tsetse fly population dynamics, accounting for combined effects of spatial complexity, density-dependence, and temperature on the age-structured population, and parametrized with field and laboratory data. We confirmed the strong impact of temperature and adult mortality on tsetse populations. We showed that the coldest cells with the smallest variations in temperature acted as refuges when adult mortality was homogeneously increased, control being less effective in such refuges. In contrast, targeting the cells contributed the most to population management, i.e. those of highest carrying capacity and the most impacted by increased mortality, resulted in a decline in population size with a similar efficacy, but resulted in more dispersed individuals, control efficacy being no longer related to temperature. Population resurgence after control was slow, but could be very high locally in refuges, with highly contrasted situations after a heterogeneous control, refuges being located at the interface between controlled and uncontrolled zones. Our results highlighted the importance of baseline data collection to characterize the targeted ecosystem before any control measure is implemented.