Just following up…
(And sorry for the double post of the question. My post disappeared when editing, then re-appeared)
I figured out that triggering do_action( 'acf/save_post', $post_id );
is the key. This means that creating a custom save function is not necessary.
add_filter( 'job_manager_update_job_data', 'my_acf_save_repeater_data', 10, 2 );
function my_acf_save_repeater_data( $post_id, $route_data ) {
do_action( 'acf/save_post', $post_id );
return $route_data;
}