This paper is concerned with a class of distributed online constrained optimization problems characterized by several key features: i) the complex coupling characteristics of multiple coupled constraints; ii) the dynamic unbalance of time-varying (TV) digraphs; iii) the nonconvex nature of local cost functions. To tackle these intricate challenges effectively, a primal dual proximal mirror descent (PDPMD) algorithm is developed. Furthermore, an auxiliary variable is employed to counteract the imbalance induced by TV directed graphs. Additionally, we prove that the proposed method, under some mild conditions, reaches stationary points with a sublinear convergence rate. At last, a numerical example is used to illustrate the validity of the proposed algorithm.