What if your private instances are not register automatically to your Load balancer target group ?

If the Loadbalancer ip(public) and the instance behind the loadbalancer are in the same avaiability zone, Autoscaling will create the instance automatically and register the instances in coresponding target groups(which are in turn used by your load balancer). You don't need to manually register instances to your target group. If you had to manually register the booting instance, something is wrong. Check the VPC and subnet of Load balancer and ASG network section.