There is much evidence that the Lapita people took R. exulans along for food. Unlike European rats, Dr. Matisoo-Smith said, exulans do not swim and dislike wet conditions. So it is unlikely that they accidentally reached the islands through infested ships.
As a food source, the rats do not require much effort. The Lapita would have just had to release them on the islands they settled, and rats being rats, there would soon be plenty for eating.
Quite a few science fiction writers have based their "space faring cultures" on the Polynesian peoples. Using a bioform to prepare a habitat (thereby wiping out many local species) for colonization is a classic terraforming move.