Drupal - Rebuild form AFTER ajax callback has run

You could try like this making submit different and callback different and see if it helps.

$form['save'] = array(
    '#type' => 'button',
    '#submit' => array('emtr_shift_plan_form_ajax_submit'),
    '#value' => 'Save',
    '#ajax' => array(
        'callback' => 'emtr_shift_plan_form_ajax',
        'wrapper' => 'postions',
    ),
    '#id' => 'ajax-save-form-values',
);

function emtr_shift_plan_form_ajax($form, &$form_state){
  return $form['positions'];
}
function emtr_shift_plan_form_ajax_submit($form, &$form_state) {

    ddl('ajax submit'); // log the ajax callback is being called

    $form_state['rebuild'] = TRUE; // As the form has already been rebuilt at this point what effect can this have?!?

    emtr_shift_plan_form_save($form, $form_state); // save the values

    // This is the point at which I want the form to be rebuilt
}

I know this question is 3 years old, but I came upon it while searching for a similar issue.

You'll need to modify your approach to get this working. The order of operations when you submit the AJAX request is this:

1. AJAX submit callback is fired. In your AJAX submit callback you'll want to save the data. Flag it in your $form_state variable.
2. Form is rebuilt.
3. AJAX callback is fired.

I've re-worked your code a little bit to demonstrate.

// AJAX FLOW: 2. Form rebuild is fired.
function emtr_shift_plan_form($form, &$form_state) {

    ddl('build'); // log that this function is being called

    $form['save'] = array(
        '#type' => 'button',
        '#submit' => array('emtr_shift_plan_form_button_submit'),
        '#value' => 'Save',
        '#ajax' => array(
            'callback' => 'emtr_shift_plan_form_ajax',
            'wrapper' => 'postions',
        ),
        '#id' => 'ajax-save-form-values',
    );

    $form['postions'] = array(
        '#type' => ' container',
        '#prefix' => '<div id="postions">',
        '#suffix' => '</div>',
    );

    // code here to populate the positions container
    if (isset($form_state['saved_values'])) {
      // do stuff.
    }
}

// AJAX FLOW: 1. Button submit is fired.
function emtr_shift_plan_form_button_submit($form, &$form_state) {

  // log the ajax callback is being called
  ddl('ajax submit');

  // save the values. Make sure the data is stored somehow so your form can get at it.
  $form_state['saved_values'] = emtr_shift_plan_form_save($form, $form_state);

  // rebuild flag here will trigger emtr_shift_plan_form() to be run
  $form_state['rebuild'] = TRUE;
}

// AJAX FLOW: 3. Button callback is fired.
function emtr_shift_plan_form_ajax($form, &$form_state) {
    return $form['positions'];
}

Hope that sheds some light for someone.