-어야 means only when that condition is met, and 오다 is coming. So: he only comes when he has time, it won't arrive until next week, will she only come once autumn is here, Koreans only come if you call them. Half the lines here are one proverb, 가는 말이 고와야 오는 말이 곱다 — the words that come back are kind only if the words you sent were.