The 39 ka Campanian Ignimbrite (CI) super-eruption was the largest volcanic eruption of the past 200 ka in Europe. Tephra deposits indicate two distinct plume forming phases, Plinian and co-ignimbrite, characteristic of many caldera-forming eruptions. Previous numerical studies have characterized the eruption as a single-phase event, potentially leading to inaccurate assessment of eruption dynamics. To reconstruct the volume, intensity, and duration of the tephra dispersal, we applied a computational inversion method that explicitly accounts for the Plinian and co-ignimbrite phases and for gravitational spreading of the umbrella cloud. To verify the consistency of our results, we performed an additional single-phase inversion using an independent thickness dataset. Our better-fitting two-phase model suggests a higher mass eruption rate than previous studies, and estimates that 3/4 of the total fallout volume is co-ignimbrite in origin. Gravitational spreading of the umbrella cloud dominates tephra transport only within the first hundred kilometres due to strong stratospheric winds in our best-fit wind model. Finally, tephra fallout impacts would have interrupted the westward migration of modern hominid groups in Europe, possibly supporting the hypothesis of prolonged Neanderthal survival in South-Western Europe during the Middle to Upper Palaeolithic transition.