It looks like at least in this study it depicts the dopamine levels are observed to drop in REM sleep disorder without much of a reason why.
http://www.sciencedaily.com/releases/2011/07/110729175617.htm
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The new study applied brain SPECT to conclude that the levels of dopamine in the brain are quickly lowering over the years in patients with REM sleep behaviour disorder. This neuroimaging technique becomes the first tool to detect the disease progression at an early stage. The first author of the three articles is Dr. Àlex Iranzo, doctor from the Neurology Service at the Hospital Clínic of Barcelona, researcher at the Biomedical Research Institute of August Pi i Sunyer (IDIBAPS) and member of the Multidisciplinary Sleep Disorders Unit , and the senior authors were to Dr. Joan Santamaria and Dr. Eduard Tolosa, from the same institution.
The study involved comparing for three years the evolution of brain SPECT in 20 patients with REM disorder and 20 healthy controls. The neuroimaging technique measures the presence of dopamine in the
substantia nigra, a part of the brain associated with learning and harmony of body movements. In Parkinson's disease a deficiency of dopamine in the
substantia nigra causes tremor, stiffness and movement slowness in patients. Results show that after 3 years of monitoring the production of dopamine in the control group was reduced by 8% due to age, while the group of REM sleep disorder patients experienced a reduction of 20%. Once the 3 year follow-up ended, 3 of 20 patients in the REM sleep disorder group had developed Parkinson's disease and their dopamine reduction was around 30%.
The three works led by the IDIBAPS -- Hospital Clínic of Barcelona team conclude that more efforts are needed to create neuroprotective drugs that prevent the progression from REM sleep behavior disorders to Parkinson's disease. For the first time scientists have a technique, brain SPECT, to evaluate whether these drugs are effective. Authors of the study suggest that, to be considered effective, a neuroprotective drug should significantly prevent the dopamine concentration from dropping in these patients."
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Another study:
University of Michigan - Neurology
http://www.hscareers.com/news/articles.asp?id=495
"Medication used to treat the disorder stimulates the production of dopamine. "We found a very strong correlation between the severity of the sleeping disorder and the level of decrease of dopamine"
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I still didn't quite find out the 'how' you are asking in the question, but it does look like increasing levels of dopamine through medication assists in treating REM sleep disorders.
