AWS won't know this IP range and won't route it. So K8s automatically populates your routing table with the routes every time a node changes or is added/removed.
K8s will give a /24 CIDR to each minion host, so the first will get 10.0.1.0/24, the next 10.0.2.0/24, and so on. Each pod will get 10.0.1.1, 10.0.1.2, etc.
Obviously having an additional IP/interface per box adds complexity, but I don't know if K8s supports any other automatic mode of operation on AWS.
(Note: Kubernetes expects AWS objects that it can control — security groups, instances, etc. — to be tagged with KubernetesCluster=<your cluster name>. This also applies to the routing table.)