Adding to a repeater is slightly different to updating a field. Check the docs
Basically, when you loop through your API data (foreach), you need to use something like:
$row = array(
'image' => 123,
'alt' => 'Another great sunset',
'link' => 'http://website.com'
);
add_row('images', $row);
Just amend the fields to suit your needs.
