What "coupling" between these networks actually measures
The default mode network is a set of brain regions that tend to be busier when you are resting or thinking inward than when you are working on a demanding external task. Early resting-state imaging found that these regions are strongly connected to one another, and that key nodes of the network show inverse correlations with lateral prefrontal regions that ramp up during a working-memory task [3]. That inverse relationship is what people mean by an "anticorrelated network": when one side is active, the other tends to be suppressed.
So "coupling" here is not a physical wire. It is a statistical tendency for two sets of brain areas to rise and fall together, or in opposition, measured while a person rests or performs a task [3]. A change in coupling means the balance of that relationship has shifted, not that a new connection appeared.
Mind wandering shifts the balance inside the default mode network
When people read while being pulled toward personal memories, the two mental states compete: reported focus on the primary task drops, comprehension of the text falls, and the retrieved memories become less vivid [1]. On the brain side, reading and autobiographical memory retrieval recruit different parts of the default mode network. Reading engaged lateral temporal and prefrontal regions falling within the network's dorsomedial subsystem, while memory retrieval engaged core regions such as medial prefrontal cortex, posterior cingulate cortex and angular gyrus [1].
The more telling difference is in how those regions connect to visual cortex. Default mode regions linked to reading were more strongly coupled to ventral visual areas than the memory-linked regions were, and people who generated more mind-wandering content and understood less showed greater decoupling between reading-related default mode sites and primary visual cortex [1]. In other words, the signature of drifting away from the text was a loosening of the tie between the reading part of the default mode network and the visual machinery that takes in the words.
What would actually separate mind wandering from other off-task states
The clearest evidence so far points to a within-network story: mind wandering while reading looks like a switch toward memory-based default mode regions that are relatively insulated from visual input, at the expense of default mode regions wired to the visual stream [1]. That is a difference in which part of the network is driving, and how tightly it is linked to the senses, rather than a simple on/off of the whole network.
To know whether coupling with the anticorrelated network is the distinguishing feature, studies would need to compare mind wandering directly against other off-task states, such as inattention or lapses without spontaneous thought, on the same coupling measure. The available work establishes that default mode activity rises during off-task thought [2] and that the network's anticorrelated relationship is real and measurable [3], but it does not yet close that gap.
Sources used in this answer
Author response: Perceptual coupling and decoupling of the default mode network during mind-wandering and reading
During reading, autobiographical memory retrieval and reading recruit different default mode subsystems, and greater decoupling between reading-related default mode sites and visual cortex is associated with more mind-wandering content and poorer comprehension.
Beyond mind wandering: Performance variability and neural activity during off-task thought and other attention lapses
Off-task thought is accompanied by increased default mode network activation, and the study compares neural activity across attention states but does not examine default-mode-to-anticorrelated-network coupling.
Functional connectivity in the resting brain: A network analysis of the default mode hypothesis
Resting-state imaging shows the default mode network is internally coupled and that its key nodes are inversely correlated with lateral prefrontal regions active during a working-memory task.
Probing the neural signature of mind wandering with simultaneous fMRI-EEG and pupillometry
Mind wandering is associated with altered default mode network activity and elevated activity in its anticorrelated network, signals that help distinguish on-task from off-task states.
Cognitive flexibility in and out of the laboratory: task switching, sustained attention, and mind wandering
The review notes that default mode network activity is higher during mind wandering and off-task states and discusses negative correlations involving the network, without explicitly contrasting mind wandering with other off-task states.
