We study the non-collinear exchange coupling across the trilayer magnetic junction composed of an intermediate layer with Rashba interaction and two sandwiching ferromagnetic ones. To compute the mediated exchange coupling between the ferromagnetic layers, one needs to go beyond the single-particle argument and numerically integrates over contributions from the whole Fermi surface. We found interesting competition between the oscillatory Ruderman-Kittel-Kasuya-Yosida and the non-collinear spiral interactions. Surprisingly, the Fermi surface topology determines which type of magnetic interaction becomes dominant. Finally, we also discuss potential applications for the non-collinear exchange coupling across the junction.