The formation of species in the absence of geographic barriers (i.e. sympatric speciation) remains one of the most controversial topics in evolutionary biology. While theoretical models have shown that this most extreme case of primary divergence-with-gene-flow is possible, only a handful of accepted empirical examples exist. And even for the most convincing examples uncertainties remain; complex histories of isolation and secondary contact can make species falsely appear to have originated by sympatric speciation. This alternative scenario is notoriously difficult to rule out. Midas cichlids inhabiting small and remote crater lakes in Nicaragua are traditionally considered to be one of the best examples of sympatric speciation and lend themselves to test the different evolutionary scenarios that could lead to apparent sympatric speciation since the system is relatively small and the source populations known. Here we reconstruct the evolutionary history of two small-scale radiations of Midas cichlids inhabiting crater lakes Apoyo and Xiloá through a comprehensive genomic data set. We find no signs of differential admixture of any of the sympatric species in the respective radiations. Together with coalescent simulations of different demographic models our results support a scenario of speciation that was initiated in sympatry and does not result from secondary contact of already partly diverged populations. Furthermore, several species seem to have diverged simultaneously, making Midas cichlids an empirical example of multispecies outcomes of sympatric speciation. Importantly, however, the demographic models strongly support an admixture event from the source population into both crater lakes shortly before the onset of the radiations within the lakes. This opens the possibility that the formation of reproductive barriers involved in sympatric speciation was facilitated by genetic variants that evolved in a period of isolation between the initial founding population and the secondary migrants that came from the same source population. Thus, the exact mechanisms by which these species arose might be different from what had been thought before.