New Twiddle

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend({
	shared: Ember.inject.service()  
});

router.js

import EmberRouter from '@ember/routing/router';
import config from './config/environment';

const Router = EmberRouter.extend({
  location: 'none',
  rootURL: config.rootURL
});

Router.map(function() {
  this.route('foo');
  this.route('bar');
});

export default Router;

routes.bar.js

import Ember from 'ember';

export default Ember.Route.extend({
  shared: Ember.inject.service(),
  
  model() {
    return Ember.get(this, 'shared.doSomething').perform();
  }
});

routes.foo.js

import Ember from 'ember';

export default Ember.Route.extend({
  shared: Ember.inject.service(),
  
  model() {
    return Ember.get(this, 'shared.doSomething').perform();
  }
});

services.shared.js

import Ember from 'ember';
import { task, timeout } from 'ember-concurrency';

export default Ember.Service.extend({
  doSomething: task(function*() {
    yield timeout(1000);
  }).drop()
});

templates.application.hbs

<div>Task state: {{shared.doSomething.state}}</div>

<p>
  Transition between the two routes before the task finishes to see the issue.
</p>

<br>
<br>

{{#link-to "foo"}}Foo{{/link-to}}
{{#link-to "bar"}}Bar{{/link-to}}

<br>
<br>

{{outlet}}

templates.bar.hbs

<h1>Bar</h1>

templates.foo.hbs

<h1>Foo</h1>

twiddle.json

{
  "version": "0.15.0",
  "EmberENV": {
    "FEATURES": {}
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.js",
    "ember": "3.2.2",
    "ember-template-compiler": "3.2.2",
    "ember-testing": "3.2.2"
  },
  "addons": {
    "ember-data": "3.2.0",
    "ember-concurrency": "0.8.19"
  }
}