The packages from mongodb.org have different names and the service has a different name. Changed the role to cover both cases.

mongodb-org/defaults/main.yml

@@ -17,16 +17,24 @@ mongodb_upgrade_from_older_version: False
 mongodb_version: 3.6
 # Set to 'latest' if you want to get the latest available package
 mongodb_pkg_state: present
-mongodb_server_pkgs:
+mongodb_server_pkgs_external_repo:
   - mongodb-org
   - mongodb-org-mongos
   - mongodb-org-server
   - mongodb-org-shell
   - mongodb-org-tools
 
-mongodb_client_pkgs:
+mongodb_client_pkgs_external_repo:
   - mongodb-org-shell
 
+mongodb_server_pkgs:
+  - mongodb
+  - mongodb-server
+  - mongo-tools
+
+mongodb_client_pkgs:
+  - mongodb-clients
+
 mongodb_start_server: 'yes'
 mongodb_tcp_port: 27017
 mongo_bind_ip: 0.0.0.0

mongodb-org/handlers/main.yml

@@ -1,5 +1,9 @@
 ---
-- name: Restart mongodb
+- name: Restart mongod
   service: name=mongod state=restarted
   when: "'{{ mongodb_start_server }}' == 'yes'"
  
+- name: Restart mongodb
+  service: name=mongodb state=restarted
+  when: "'{{ mongodb_start_server }}' == 'yes'"
+ 

mongodb-org/tasks/mongodb.yml

@@ -13,52 +13,78 @@
         - mongodb_start_server == 'no'
         - mongodb_install_conf
 
-  when: mongodb_install_server
+  when:
+    - mongodb_install_server
+    - mongodb_install_from_external_repo
   tags: mongodb 
 
 - block:
-    - name: Install the mongodb apt keys
+    - name: Install the mongodb-org apt keys
       apt_key: keyserver='hkp://keyserver.ubuntu.com:80' id={{ item }} state=present
       with_items: '{{ mongodb_repo_keys }}'
       when: mongodb_install_from_external_repo
       register: apt_key_update_cache
 
-    - name: Update the apt cache after adding a new key
+    - name: Remove the old mongodb-org apt repositories
-      apt: update_cache=yes
-      when: apt_key_update_cache is changed
-
-    - name: Remove the old mongo apt repositories
       apt_repository: repo='{{ item }}' state=absent update_cache=yes
       with_items: '{{ mongodb_old_repositories }}'
       when: mongodb_upgrade_from_older_version
 
-    - name: Install the mongodb repository
+    - name: Install the mongodb-org repository
       apt_repository: repo="{{ mongodb_apt_repository }}" update_cache=yes state=present
 
-  when: mongodb_install_from_external_repo 
+    - name: Install/Update the mongodb-org configuration
-  tags: [ 'mongodb', 'mongodb_client', 'mongodb_repo' ]
-
-- block:
-    - name: Install/Update the mongodb configuration
       template: src=mongod-{{ mongodb_version }}.conf.j2 dest=/etc/mongod.conf owner=root group=root mode=0444 backup=yes
       when: mongodb_install_conf
       notify: Restart mongodb
+      tags: [ 'mongodb', 'mongodb_update_conf' ]
 
-  when: mongodb_install_server 
+  when:
-  tags: [ 'mongodb', 'mongodb_update_conf' ]
+    - mongodb_install_server 
+    - mongodb_install_from_external_repo 
+  tags: [ 'mongodb' ]
+
+- block:
+    - name: We are upgrading, install the latest version of the mongodb-org packages, external repository
+      apt: pkg={{ mongodb_server_pkgs_external_repo }} state=latest update_cache=yes cache_valid_time=1800
+      when: mongodb_upgrade_from_older_version
+
+    - name: Install the mongodb-org packages, external repository
+      apt: pkg={{ mongodb_server_pkgs_external_repo }} state={{ mongodb_pkg_state }} update_cache=yes cache_valid_time=1800
+
+    - name: Install the mongodb-org defaults file
+      template: src=mongod-default.j2 dest=/etc/default/mongod owner=root group=root mode=0444
+      when: mongodb_install_conf
+      notify: Restart mongod
+      tags: [ 'mongodb', 'mongodb_update_conf' ]
+
+  when:
+    - mongodb_install_server 
+    - mongodb_install_packages
+    - mongodb_install_from_external_repo 
+  tags: mongodb
 
 - block:
     - name: We are upgrading, install the latest version of the mongodb packages
       apt: pkg={{ mongodb_server_pkgs }} state=latest update_cache=yes cache_valid_time=1800
-      when:
+      when: mongodb_upgrade_from_older_version
-        - mongodb_install_packages
-        - mongodb_upgrade_from_older_version
 
     - name: Install the mongodb packages
       apt: pkg={{ mongodb_server_pkgs }} state={{ mongodb_pkg_state }} update_cache=yes cache_valid_time=1800
-      when:
-        - mongodb_install_packages
 
+    - name: Install/Update the mongodb configuration
+      template: src=mongod-{{ mongodb_version }}.conf.j2 dest=/etc/mongodb.conf owner=root group=root mode=0444 backup=yes
+      when: mongodb_install_conf
+      notify: Restart mongodb
+      tags: [ 'mongodb', 'mongodb_update_conf' ]
+
+  when:
+    - mongodb_install_server 
+    - mongodb_install_packages
+    - not mongodb_install_from_external_repo 
+  tags: mongodb
+
+- block:
     - name: Create the mongodb log directory
       file: dest={{ mongodb_logdir }} state=directory owner={{ mongodb_user }} group={{ mongodb_group }} mode=0755
       when: mongodb_install_conf
@@ -67,25 +93,39 @@
       file: dest={{ mongodb_dbpath }} state=directory owner={{ mongodb_user }} group={{ mongodb_group }} mode=0755
       when: mongodb_install_conf
 
-    - name: Install the mongodb defaults file
-      template: src=mongod-default.j2 dest=/etc/default/mongod owner=root group=root mode=0444
-      when: mongodb_install_conf
-      notify: Restart mongodb
-
     - name: Install the cron job that manages log files rotation
       template: src=mongo_log_rotate.sh.j2 dest=/etc/cron.daily/mongo_log_rotate owner=root group=root mode=0555
       when: not mongodb_systemlog_external_logrotate
 
-    - name: Ensure mongodb is started and enabled
-      service: name=mongod state=started enabled=yes
-      when: ( mongodb_start_server is defined ) and ( mongodb_start_server == 'yes' ) and ( mongodb_install_conf )
-
   when: mongodb_install_server
   tags: mongodb
 
+- block:
+    - name: Ensure mongodb is started and enabled
+      service: name=mongodb state=started enabled=yes
+
+  when:
+    - mongodb_install_server 
+    - mongodb_start_server == 'yes'
+    - not mongodb_install_from_external_repo 
+  tags: mongodb
+
+- block:
+    - name: Ensure mongodb-org is started and enabled
+      service: name=mongod state=started enabled=yes
+
+  when:
+    - mongodb_install_server 
+    - mongodb_start_server == 'yes'
+    - mongodb_install_from_external_repo 
+  tags: mongodb
+
 - block:
     - name: Install the mongodb client packages
       apt: pkg={{ mongodb_client_pkgs }} state={{ mongodb_pkg_state }} update_cache=yes cache_valid_time=1800
 
+    - name: Install the mongodb client packages, external repository
+      apt: pkg={{ mongodb_client_pkgs_external_repo }} state={{ mongodb_pkg_state }} update_cache=yes cache_valid_time=1800
+
   when: not mongodb_install_server
   tags: [ 'mongodb', 'mongodb_client' ]