We introduce a simple model consisting of two sites interacting with a common global environment. After showing how to analytically construct the matrix product operator representation of a Hamiltonian with long-range interactions—thus enabling the use of loop-free tensor networks without swap-gates—we scrutinize the environment dynamics to uncover the origin of a back-flow of information inducing (potentially periodic) non-Markovian initial state population revivals on a new time-scale set by the spatial structure of the system.