We present a continuous time random walk (CTRW) model for the kinetics of pseudo-first-order long-range reactions in zeolites assisted by migration between the adsorption sites. Both Markovian and non-Markovian formulations admit a simple matrix solution in terms of the lattice Green's function. Diffuse-reflectance transient absorption study of triplet anthracene quenching by azulene in NaY zeolite is reported giving a direct visual indication of the long-range reaction between molecules residing in the neighboring cages, reflecting an open structure of the cage network. The Markovian model with unbiased nearest-neighbor CTRW on a diamond lattice of NaY supercages explains the experimental decay data. This practical example demonstrates a general possibility to consistently recover information about intercage transport in zeolites and related microporous materials by using an indicator reaction and an appropriate theoretical interpretation, complementary to conventional NMR techniques.