We present the fragmentation dynamics of CsC_n^– (n≤10) in collision with argon at 15 keV impact energy. The propensity for the formation of the fragment ions C_m^– (m≤n) exhibits even-odd oscillations, with the yield being larger when m is even; and this is correlated with the larger electron affinity of the product ion when m is even. We observe C₃ loss in the case of CsC₉^– clusters. We find an unexpected oscillatory pattern in the kinetic-energy release (KER) spectra of C_n^– fragments. The ratio of the width of C_n^– to the parent CsC_n^–, which is a measure of the KER in the center-of-mass (c.m.) frame, shows even-odd oscillation, with the ratio being larger when n is even than when n is odd. The oscillatory pattern is correlated with differences in fragmentation pathways accessed in the Franck-Condon region. Applying the reflection method with model potentials for two different   fragmentation paths, we find that the KER in the c.m. frame oscillates if an ion-pair formation pathway is preferred for clusters of even n.