initial properties

components.task-tree.js

import Ember from 'ember';

export default Ember.Component.extend({
  isExpanded: false,
  isExpandedAtFirst: false,
  
  init() {
    this._super(...arguments)
    this.set('isExpanded', this.get('isExpandedAtFirst'))
  },
  
  actions: {
    toggleIsExpanded() {
      this.toggleProperty('isExpanded')
    }
  }
});

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend({
  appName: 'Ember Twiddle',
  config1: {isExpandedAtFirst: true},
  config2: {isExpandedAtFirst: false}
});

templates.application.hbs

{{#task-tree isExpandedAtFirst=config1.isExpandedAtFirst}}some content expanded by default{{/task-tree}}

{{#task-tree isExpandedAtFirst=config2.isExpandedAtFirst}}some content hidden by default{{/task-tree}}

templates.components.task-tree.hbs

{{#if isExpanded}}
<button onclick={{action 'toggleIsExpanded'}}>hide</button>
{{yield}}
{{else}}
<button onclick={{action 'toggleIsExpanded'}}>show</button>
{{/if}}

twiddle.json

{
  "version": "0.13.1",
  "EmberENV": {
    "FEATURES": {}
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "2.16.2",
    "ember-template-compiler": "2.16.2",
    "ember-testing": "2.16.2"
  },
  "addons": {
    "ember-data": "2.16.3"
  }
}