About context. It is a sentence from an anime series (charlotte). One of the characters proposes their actions regarding other character (Ayumi, 歩未ちゃん).
Here we have 歩未ちゃんへの注意 (attention to Ayumi). And the sentence says to stress (...を促す) this attention. So I guess the meaning is to make the teacher watch Ayumi closely but how does に work here? Is the idea similar to something like "ジョンに花をあげました。" But instead of flowers we have attention and instead of giving (あげる) we have stressing (促す)?