I don't find any publications referring to a river on Poro Island, and from your description I agree it's not a river.

Also, if it were then Rarotonga at 67.39 km2 has a waterfall ending up in a pond. https://www.gettyimages.com/detail/photo/wigmores-papua-wate... . Video after a heavy rainfall at https://www.youtube.com/watch?v=AgM7b8WjCPw .