The temperature dependence of the electron-spin lifetime T1 and the g factor are anomalous in alkali fullerides (K,Rb)3C60, which cannot be explained by the canonical Elliott-Yafet theory. These materials are archetypes of strongly correlated and narrow band metals. We introduce the concept of a "complex electron-spin resonance frequency shift" to treat these measurables in a unified manner within the Kubo formalism. The theory is applicable for metals with nearly degenerate conduction bands and large momentum scattering even with an anomalous temperature dependence and sizable residual value.