Theoretical analysis of the stopped-flow fluorescence time-scan method, as applied for studying the exchange dynamics in micelle solutions, is presented on the basis of the stochastic model of solubilization. Different exchange mechanisms are considered with a focus on the collisional one-particle hopping, where the exact solution for the experimentally observable relaxation function is obtained, and the fusion-fission. It is emphasized that whatever the mechanism of exchange is, the long-time relaxation rate constant is independent of the initial condition in the stopped-flow mixing.