mongoose nested documents

I have 2 schemas set up in mongoose:

var Job = new mongoose.Schema({
    title: String,
    budget: Number
});

var JobModel = mongoose.model('Job', Job);

var Customer = new mongoose.Schema({
    name: String,
    jobs: [Job]
});

var CustomerModel = mongoose.model('Customer', Customer);

The Customer model has an array of job models.

I am adding a new job as follows:

app.post('/api/jobs', function(req, res){

    var job = new JobModel({
        title: req.body.title,
        budget: req.body.budget
    });

    job.save(function(err){
        if(!err){
            CustomerModel.findById(req.body.customerId, function(err, customer){
                if(!err){
                    customer.jobs.push(job);
                    customer.save(function(err){
                        if(!err){
                            return console.log('saved job to customer');
                        }
                    });
                }
            });
            return console.log('created job');

        } else {
            return console.log(err);
        }
    });

    return res.send(job);
});

When I add a new job and GET all the customers I get which I think is correct:

[{
    "__v": 1,
    "_id": "50f85695771aeeda08000001",
    "name": "Customer1",
    "jobs": [
      {
        "_id": "50fad6985edd968840000002",
        "budget": 100,
        "title": "job1"
      }
    ]
  }, ...]

Now if I update job1, and GET all the jobs, job 1 has been updated (budget is now 500)

[{
    "title": "job1",
    "budget": 500,
    "_id": "50fad6985edd968840000002",
    "__v": 0
  }, ...]

but the job1 in the customers job array remains unchanged.

 [{
        "__v": 1,
        "_id": "50f85695771aeeda08000001",
        "name": "Customer1",
        "jobs": [
          {
            "_id": "50fad6985edd968840000002",
            "budget": 100,
            "title": "job1"
          }
        ]
      }, ...]

Do I therefore need to search the Customer1's job array and find the job1 job and update that also every time I update or delete or am I totally doing the whole nesting thing the wrong way?

I get that the jobs array in customer is an array of objects but I thought that they may be some how just a reference copy of the job rather than a duplicate??