The role it plays in those chronic illnesses are seemingly due to melatonin's role in maintaining the sleep-wake cycle. Disruption of that bodily circadaen rhythem is thought to increase the likelihood of cancer, diabetes, heart disease etc.

It's not about the intracellular concentration of melatonin, it's variable and is cycled every day. It's more about activation of the melatonin receptors at the wrong time and disruption of the circadaen rhythem. At least that was how I understood the paper.