A K-tier heterogeneous mmWave uplink cellular network with user-centric small cell deployments is considered in this paper. In particular, the user equipments (UEs) are assumed to be clustered around small-cell base stations (BSs) according to the Thomas cluster process. Practical line-of-sight (LOS) and none-line-of-sight (NLOS) models are adopted with different parameters for different tiers. In this setting, we consider a coupled association probability model, and derive the probability that the BSs of each tier are associated with UEs from each cluster. Following the identification of the association probabilities, we characterize the Laplace transforms of the inter-cell interferences in closed-form. Using tools from stochastic geometry, we provide a general expression of the SINR coverage probability in each tier. Via numerical and simulation results, we confirm the analysis and the derived expressions, and investigate the impact of important system parameters.