The article from the "Shoku Nihongi" (Chronicle of Japan Continued) explains the reason for receiving such an reward as simply 'contributions in Jinshin War'; however, judging from other articles in the same book, such awards were usually received after death, and therefore this was probably the case for Kimite as well.
これを伝える『続日本紀』の記事は「壬申の功臣」としか理由を伝えないが、他の例で壬申の功臣への賜位記事は死亡時の追贈であるから、この場合も同じと考えられる。