There is a hook that is fired when a repeater is added, this is in JavaScript. See Adding custom javascript to fields and JavaScript API. The hook you are looking for is append.
acf/load_field and other hooks should use the field key variation for repeater sub fields. However, most of these hooks only fire once per sub field. The acf/prepare_field fires on every instance, but this only fires for existing fields and will not work when a row is added to a repeater. There is also no way of telling what row of the repeater is being prepared for render.
Without using JavaScript you would have to do what you describe in your last statement about using acf/save_post.
