The recently introduced concept of dynamic communicability is a valuable tool for ranking the importance of nodes in a temporal network. Two metrics, broadcast score and receive score, were introduced to measure the centrality of a node with respect to a model of contagion based on time-respecting walks. This article examines the temporal and structural factors influencing these metrics by considering a versatile stochastic temporal network model. We analytically derive formulae to accurately predict the expectation of the broadcast and receive scores when one or more columns in a temporal edge-list are shuffled. These methods are then applied to two publicly available data-sets and we quantify how much the centrality of each individual depends on structural or temporal influences. From our analysis we highlight two practical contributions: a way to control for temporal variation when computing dynamic communicability, and the conclusion that the broadcast and receive scores can, under a range of circumstances, be replaced by the row and column sums of the matrix exponential of a weighted adjacency matrix given by the data.