As an addition to johnharris85 DNS, when you will separate your apps, which you should do in your scenario.

Multi-container Pods are usually used in specific use cases, like for example sidecar containers to help the main container with some particular tasks or proxies, bridges and adapters to for example provide connectivity to some specific destination.

In your case you can easily separate them. In this case you have a deployment with 1 Pod in which there are 3 containers which communicate with each other by localhost and not DNS names as already mentioned. After which I recommend you to read about DNS inside of Kubernetes and how the communication works with the services stepping up into the game. In case of pods you can read more here.

You have defined all 3 containers as part of the same pod. Pods have a common network namespace so in your current setup (which is not correct, more on that in a second), you could talk to the other containers using localhost:<port>.

The 'correct' way of doing this would be to create a deployment for each application, and front those deployments with services.

Your example would roughly become (untested):

kind: Deployment
apiVersion: apps/v1
metadata:
  name: my-api-node
  namespace: my-api
  labels:
    app: my-api-node
spec:
  replicas: 1
  selector:
    matchLabels:
      app: my-api-node
  template:
    metadata:
      name: my-api-node
      labels:
        app: my-api-node
    spec:
      containers:
      - name: my-api-node
        image: my-api-node
        command: ["npm"]
        args: ["run", "start-docker-dev"]
        ports:
        - containerPort: 3000
---
apiVersion: v1
kind: Service
metadata:
  namespace: my-api
  name: my-api-node
spec:
  selector:
    app: my-api-node
  ports:
  - protocol: TCP
    port: 3000
    targetPort: 3000
---
kind: Deployment
apiVersion: apps/v1
metadata:
  name: my-api-redis
  namespace: my-api
  labels:
    app: my-api-redis
spec:
  replicas: 1
  selector:
    matchLabels:
      app: my-api-redis
  template:
    metadata:
      name: my-api-redis
      labels:
        app: my-api-redis
    spec:
      containers:
      - name: my-api-redis
        image: redis:5.0.4-alpine
        command: ["redis-server"]
        args: ["--appendonly", "yes"]
        ports:
        - containerPort: 6379
---
apiVersion: v1
kind: Service
metadata:
  namespace: my-api
  name: my-api-redis
spec:
  selector:
    app: my-api-redis
  ports:
  - protocol: TCP
    port: 6379
    targetPort: 6379
---
kind: Deployment
apiVersion: apps/v1
metadata:
  name: my-api-postgres
  namespace: my-api
  labels:
    app: my-api-postgres
spec:
  replicas: 1
  selector:
    matchLabels:
      app: my-api-postgres
  template:
    metadata:
      name: my-api-postgres
      labels:
        app: my-api-postgres
    spec:
      containers:
      - name: my-api-postgres
        image: postgres:11.2-alpine
        env:
        - name: POSTGRES_USER
          value: "my-api"
        - name: POSTGRES_DB
          value: "my-api"
        - name: POSTGRES_PASSWORD
          value: "my-pass"
        ports:
        - containerPort: 5432
---
apiVersion: v1
kind: Service
metadata:
  namespace: my-api
  name: my-api-postgres
spec:
  selector:
    app: my-api-postgres
  ports:
  - protocol: TCP
    port: 5432
    targetPort: 5432

DNS records get registered for services so you are connecting to those and being forwarded to the pods behind it (simplified). If you need to get to your node app from the outside world, that's a whole additional deal, and you should look at LoadBalancer type services, or Ingress.