Müllerian mimicry among Neotropical Heliconiini butterflies is an excellent example of natural selection, and is associated with the diversification of a large continental-scale radiation. Some of the processes driving the evolution of mimicry rings are likely to generate incongruent phylogenetic signals across the assemblage, and thus pose a challenge for systematics. We use a dataset of 22 mitochondrial and nuclear markers from 92% of species in the tribe to re-examine the phylogeny of Heliconiini with both supermatrix and multi-species coalescent approaches, characterise the patterns of conflicting signal and compare the performance of various methodological approaches to reflect the heterogeneity across the data. Despite the large extent of reticulate signal and strong conflict between markers, nearly identical topologies are consistently recovered by most of the analyses, although the supermatrix approach fails to reflect the underlying variation in the history of individual loci. The first comprehensive, time-calibrated phylogeny of this group is used to test the hypotheses of a diversification rate increase driven by the dramatic environmental changes in the Amazonia over the past 23 million years, or changes caused by diversity-dependent effects on the rate of diversification. We find that the tribe Heliconiini had doubled its rate of speciation around 11 Ma and that the presently most speciose genus Heliconius started diversifying rapidly at 10 Ma, likely in response to the recent drastic changes in topography of the region. Our study provides comprehensive evidence for a rapid adaptive radiation among an important insect radiation in the most biodiverse region of the planet.