Not such a simple and clear pattern
What you are talking about is called insular dwarfism. The process is not as straight forward as you seem to think it is. It is not systematic that insular islands evolve toward reduce sizes. In fact, the opposite of insular dwarfism, insular gigantism (which is related to Foster's rule) has also been observed.
In any case, there seems that islands often bring selection pressures of size but the causes are numerous. I think wikipedia does a descent job at screening over the existing explanations.
Wiki > insular dwarfism > Factors influencing the extent of dwarfing
For both herbivores and carnivores, island size, the degree of island isolation and the size of the ancestral continental species appear not to be of major direct importance to the degree of dwarfing.4 However, when considering only the body masses of recent top herbivores and carnivores, and including data from both continental and island land masses, the body masses of the largest species in a land mass were found to scale to the size of the land mass, with slopes of about 0.5 log(body mass/kg) per log(land area/km2). There were separate regression lines for endothermic top predators, ectothermic top predators, endothermic top herbivores and (on the basis of limited data) ectothermic top herbivores, such that food intake was 7 to 24-fold higher for top herbivores than for top predators, and about the same for endotherms and ectotherms of the same trophic level (this leads to ectotherms being 5 to 16 times heavier than corresponding endotherms).
Wiki > Insular gigantism > possible causes
Large mammalian carnivores are often absent on islands because of insufficient range or difficulties in over-water dispersal. In their absence, the ecological niches for large predators may be occupied by birds, reptiles or smaller carnivorans, which can then grow to larger-than-normal size. For example, on prehistoric Gargano Island in the Miocene-Pliocene Mediterranean, on islands in the Caribbean like Cuba, and on Madagascar and New Zealand, some or all apex predators were birds like eagles, falcons and owls, including some of the largest known examples of these groups. However, birds and reptiles generally make less efficient large predators than advanced carnivorans.
Since small size usually makes it easier for herbivores to escape or hide from predators, the decreased predation pressure on islands can allow them to grow larger.1[a] Small herbivores may also benefit from the absence of competition from missing types of large herbivores.
Diagram displaying the change in size of weta species in two ecosystems. The size and population of wetas are affected by predation. Rats introduced on the mainland began to prey on wetas, reducing their population; wetas shrank in response. On an island isolated from predation, such as Little Barrier Island, wetas have a dense population and have grown to a massive size. Insular species of giant wetas are the only ones not facing extinction. As wetas grow over time, bird predation declines.
Benefits of large size that have been suggested for island tortoises include decreased vulnerability to scarcity of food and/or water, through ability to survive for longer intervals without them, or ability to travel longer distances to obtain them. Periods of such scarcity may be a greater threat on oceanic islands than on the mainland.4
Thus, island gigantism is usually an evolutionary trend resulting from the removal of constraints on the size of small animals related to predation and/or competition.5 Such constraints can operate differently depending on the size of the animal, however; for example, while small herbivores may escape predation by hiding, large herbivores may deter predators by intimidation. As a result, the complementary phenomenon of island dwarfism can also result from the removal of constraints related to predation and/or competition on the size of large herbivores. In contrast, insular dwarfism among predators more commonly results from the imposition of constraints associated with the limited prey resources available on islands. As opposed to island dwarfism, island gigantism is found in most major vertebrate groups and in invertebrates.
Territorialism may favor the evolution of island gigantism. A study on Anaho Island in Nevada determined that reptile species that were territorial tended to be larger on the island compared to the mainland, particularly in the smaller species. In territorial species, larger size makes individuals better able to compete to defend their territory. This gives additional impetus to evolution toward larger size in an insular population.
A further means of establishing island gigantism may be a founder effect operative when larger members of a mainland population are superior in their ability to colonize islands.
Island size plays a role in determining the extent of gigantism. Smaller islands generally accelerate the rate of evolution of changes in organism size, and organisms there evolve greater extremes in size.