The plain -ㄴ다 form said out loud is not a written report but a live call, and doubling it — 온다 온다 — is what you say as something approaches: food arriving at the table, someone walking up. 오신다 오신다 is the same with the honorific, for a person you respect. One line uses it differently: 비가 온다 온다 하면서 안 오다가 means everyone kept saying rain was coming and it never did.