I found the following (Below) on a site for uses for Ritalin. I couldn't find out any detailed information leading to why this med is prescribed for depression. However, it does state Ritalin is sometimes used to treat depression. Your best bet is to continue research online as there is probably much more information available indicating how Ritalin affects the neurotransmitters.
When this medication is used to treat ADHD, patients may find they have increased attention, decreased impulsiveness, and decreased hyperactivity (see also Notes section). This medication is a mild stimulant that works by affecting the levels of chemicals (neurotransmitters) in the nervous system.
This medication should not be used to treat simple fatigue symptoms.
OTHER USES: This section contains uses of this drug that are not listed in the approved professional labeling for the drug but that may be prescribed by your health care professional. Use this drug for a condition that is listed in this section only if it has been so prescribed by your health care professional.
This medication may also be used for treating depression in certain cases.