We investigate the carrier-mediated exchange coupling between two ferromagnets, sandwiching an intermediate thin layer with Rashba interaction. The effective exchange coupling is obtained by integrating out the itinerant carriers. It turns out that the magnetic trends depend sensitively upon the topology of the Fermi surface. As the topology changes from "wedding cake" to "donut", the mediated exchange goes from the oscillatory Ruderman-Kittel-Kasuya-Yosida to the non-collinear spiral interactions accordingly. It is rather surprising that the Fermi surface topology determines which type of magnetic interaction becomes dominant. Finally, we also discuss potential applications for carrier-mediated exchange coupling across the junction.