Why is hyper pigmentation the common aftermath of skin lesions and abrasions?
The upper layer of the skin (or the epidermis) is formed mostly by keratinocytes and some melanocytes (about 30-40 times more keratinocytes) and also fibroblasts (although they are not shown here). The melanocytes are found in the basal cell layer at the border between epidermis and dermis as shown in the figure below (from here):



The melanocytes spread out their dendrites between the keratinocytes and transport the melanosomes (pigment containing vacuoles) to them to pigment these cells. This is a highly regulated process and depends strongly on the interaction between keratinocytes and melanocytes. 

In the so-called paracrine pathway the keratinocytes secret substances which regulate the production of melanin. These are for example alpha-MSH or ACTH, which stimulate the melanocytes to produces more melanin.

This regulation is the key to the hyperpigmentation. During the proliferation or the inflammation chemokines and hormones are produced (and secreted) in the skin which stimulate keratinocytes and fibroblasts. These are for example the keratinocyte growth factor (KGF), as well as the chemokines IL1-alpha and TNF-alpha. This stimulation leads to the production of ACTH (and derived peptides) by the keratinocytes and the secretion of stem cell factor (SCF) and hepatocyte growth factor (HGF) by the fibroblasts which all induce pigmentation. The chemokine secretion is also enhanced from the keratinocytes by KGF. If you are interested in a deeper view at this topic, have a look at reference 1 (and the references in the paper). Reference 2 goes deeper into the regulation of the paracrine signalling.

In an injury (especially in larger areas of the skin) a lot of cells are damaged and need to be replaced. This functions via cell division but also via the migration of cells into the affected area. This is described by the paper you link - here melanocytes and melanoblasts (melanocyte stem cells which can divide and then differentiate into melanocytes) migrate into the injured region to replace the destroyed melanocytes.

References:


Mechanisms underlying post- inflammatory hyperpigmentation: lessons
from solar lentigo
Hepatocyte Growth Factor Establishes Autocrine and Paracrine
Feedback Loops for the Protection of Skin Cells after UV Irradiation