In order to avoid downtime, you have to explicitly mention rolling update strategy. i.e

spec:
  replicas: 1
  strategy:
    type: RollingUpdate
    rollingUpdate:
      maxSurge: 2        # how many pods we can add at a time
      maxUnavailable: 0  # maxUnavailable define how many pods can be unavailable
                         # during the rolling upd

Thus, secondary deployment is created with the new version of the image, then the number of replicas of the old version is decreased and the new version is increased until the correct number of replicas is reached.