Compound temperature-moisture extremes, such as droughts or hot-wet extremes, have a pronounced and sometimes long-lasting impact on vegetation productivity. Accurate simulation of the involved processes by emission-driven Earth system models (ESMs) is crucial for inferring future terrestrial carbon uptake. However, ESMs often exhibit biases in the frequency and intensity of climate and weather extremes. Their ability to reproduce observed impacts of extreme atmospheric conditions on gross primary productivity (GPP) is therefore unclear. Comprehensive assessments of the statistical link between compound events and vegetation productivity beyond individual regions or event types are rare. Here, we scrutinize the relationship between temperature-moisture extremes and exceptionally low or high vegetation productivity in two state-of-the-art ESMs, CESM2 and MPI-ESM1.2, and gauge their performance relative to observation-constrained data. We find that temperature-moisture extremes modulate vegetation productivity in observations and models. The global-scale strength and timing of the statistical relationship agree well between observation-based data and model output. However, this agreement deteriorates towards smaller spatial scales, especially in the low latitudes. Here, an overestimated coupling strength by both models, likely related to biased rates of soil moisture change, suggests potentially unrealistic evaporative feedbacks, exaggerated drainage, or inadequate effective water-holding capacity in ESMs. Nevertheless, all data sources identify coherent significant relationships for all combinations of temperature-moisture and GPP extremes. This result highlights both beneficial and detrimental influences of temperature-moisture compound events on vegetation productivity and the importance of comprehensive assessments beyond single event types for capturing the net effect of climatic extremes on the biosphere. Further research should examine whether overestimated plant productivity responses to extreme conditions are a recurring phenomenon across all Earth system models. It could also investigate non-stationarity and nonlinearity of the relationships between climatic and vegetation extremes under climate change.