We present a detailed experimental and theoretical study of the spin-exchange mechanism arising in the electronic ground states of alkali-metal vapor atoms. As opposed to the well-explored formation of a stretched state in a longitudinal magnetic field (parallel to the laser propagation direction) we employ adapted hyperfine-selective optical pumping to supress spin-exchange relaxation. By comparing measurements of the intrinsic relaxation rate of the spin coherence in the ground state of cesium atoms with detailed density-matrix simulations we show, that the relaxation due to spin-exchange collisions can be reduced substantially even in a tilted magnetic field of geomagnetic strength, the major application case of scalar magnetic surveying. This explains the observed striking improvement in sensitivity and further deepens the understanding of the light-narrowed Mx (LN) magnetometer, that was presented recently. Additionally, new avenues for investigating the dynamics in alkali atoms governed by the spin-exchange interaction and interacting with arbitrary external fields are opened up.