Measurements of the low-energy electronic structure in Gd2PdSi3 and Tb2PdSi3 by means of angle-resolved photoelectron spectroscopy reveal a Fermi surface consisting of an electron barrel at the Gamma point surrounded by spindle-shaped electron pockets originating from the same band. The calculated momentum-dependent RKKY coupling strength is peaked at the 1/2 Gamma K wave vector, which coincides with the propagation vector of the low-temperature in-plane magnetic order observed by neutron diffraction, thereby demonstrating the decisive role of the Fermi surface geometry in explaining the complex magnetic ground state of ternary rare earth silicides.