Running Time of naive implementation of Dijkstra's Algorithm
In each iteration we need to go over all edges crossing the cut $(X,V\setminus X)$. The algorithm doesn't explain how we do that, so it is difficult to analyze the exact running time, though $O(m)$ per iteration is definitely an upper bound. A naive implementation will presumably go over all edges, checking which of them cross the cut, and for this implementation, the running time will indeed be $\Theta(m)$ per iteration.