If you enable process (PID) namespace sharing for your pods, the init process (pause) will come from Kubernetes. If you have a separate process namespace for your containers, they need to include tini or another init process themselves.
According to https://www.ianlewis.org/en/almighty-pause-container, Kubernetes 1.7 had a shared process namespace by default and a kubelet flag to disable it, 1.8 had it off by default and a kubelet flag to enable it. Kubernetes 1.11 has an alpha feature to enable a shared process namespace:
https://kubernetes.io/docs/tasks/configure-pod-container/share-process-namespace/