I have the following deployment in kubernetes:

 apiVersion: extensions/v1beta1
 kind: Deployment
 metadata:
   labels:
     run: hello-node
   name: hello-node
   namespace: default
 spec:
   replicas: 2
   selector:
     matchLabels:
       run: hello-node
   strategy:
     rollingUpdate:
       maxSurge: 2
       maxUnavailable: 0
     type: RollingUpdate
   template:
     metadata:
       creationTimestamp: null
       labels:
         run: hello-node
     spec:
       containers:
       - image: <image>:<tag>
         imagePullPolicy: Always
         name: hello-node
         livenessProbe:
           httpGet:
             path: /rest/hello
             port: 8081
           initialDelaySeconds: 15
           timeoutSeconds: 1
         ports:
         - containerPort: 8081
           protocol: TCP
         resources:
           requests:
             cpu: 400m
         terminationMessagePath: /dev/termination-log
       dnsPolicy: ClusterFirst
       restartPolicy: Always
       securityContext: {}
       terminationGracePeriodSeconds: 30

The issue is that when I update my deployment to let's say a new version of my image, Kubernetes will instantly kill both pods with the old image, and bring two new pods with the new image. While the new pods are booting up I experience an interruption of service.

Because of the rollingUpdate and the livenessProbe I'm expecting Kubernetes to do the following:

1. Start one pod with the new image
2. Wait for the new pod to be healthy based on the livenessProbe
3. Kill one pod with the old image
4. Repeat until all pods have been migrated

I am missing something here?