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Time Varying Functional Connectivity (TVFC) investigates how the interactions among brain regions vary over the course of an fMRI experiment. The transitions between different individual connectivity states can be modulated by changes in underlying physiological mechanisms that drive functional network dynamics, e.g., changes in attention or cognitive effort as measured by pupil dilation. In this paper, we develop a multi-subject Bayesian framework for estimating dynamic functional networks as a function of time-varying exogenous physiological covariates that are simultaneously recorded in each subject during the fMRI experiment. More specifically, we consider a dynamic Gaussian graphical model approach, where a non-homogeneous hidden Markov model is employed to classify the fMRI time series into latent neurological states, borrowing strength over the entire time course of the experiment. The state-transition probabilities are assumed to vary over time and across subjects, as a function of the underlying covariates, allowing for the estimation of recurrent connectivity patterns and the sharing of networks among the subjects. Our modeling approach further assumes sparsity in the network structures, via shrinkage priors. We achieve edge selection in the estimated graph structures, by introducing a multi-comparison procedure for shrinkage-based inferences with Bayesian false discovery rate control. We apply our modeling framework on a resting-state experiment where fMRI data have been collected concurrently with pupillometry measurements, leading us to assess the heterogeneity of the effects of changes in pupil dilation, previously linked to changes in norepinephrine-containing locus coeruleus, on the subjects' propensity to change connectivity states.