Cause a .change () to fire when 2 inputs were modified

In order for your code to work, you will have to make some changes. In this case, just adding the onchange event to the text boxes is enough. It's just a matter of accommodating javascript functions so they run fine. I'll send you an example code of how it would look.

<script type="text/javascript">
    let status_usuario = false;
    let status_correo = false;
    $(document).ready(function($) {

        $('#usuario').change(function() {
            status_usuario = true;
            _sumbitForm();
        });

        $('#emailA').change(function() {
            status_correo = true;
            _sumbitForm();
        });

    });

    function _sumbitForm() {

        if ( status_correo==true && status_usuario==true) {
            alert('Formulario usuario con correo enviado!');
            $("#actualizar").prop("method", "post");
        }


        if ( status_correo==false && status_usuario==true ) {
            alert('Actualizar Correo');

            $("#actualizar").prop("method", "post");
            $("#emailA").prop("name", "emailNo");
        }

        if (status_correo==true && status_usuario==false ) {
            alert('Actualizar Usuario');

            $("#actualizar").prop("method", "post");
            $("#usuario").prop("name", "usuarioNo");
        }


    } //_sumbitForm
</script>

This is a concept error about how events work in JavaScript and jQuery. Let's analyze the code you have right now (simplifying it a bit):

// quieres que esto se ejecute cuando ambos input, #usuario y #emailA, cambien
$('#usuario , #emailA').change(function() {
  status_correo = true;
  status_usuario = true;
  _sumbitForm();
});

// quieres que esto se ejecute cuando #usuario cambie
$('#usuario').change(function() {
  status_usuario = true;
  _sumbitForm();
});

// quieres que esto se ejecute cuando #emailA cambie
$('#emailA').change(function() {
  status_correo = true;
  _sumbitForm();
});

The problem is that association of events is individual and not collective. So when you do $('#usuario , #emailA').change(...) , what you are doing is to associate the same action for the event change to the two elements indicated in the selector individually. That action will be executed when the event occurs for one of those elements and not when the event occurs for both.

This is important because as soon as you change the value of #usuario or #emailA (only one), making status_correo = true; and status_usuario = true; is as if you had both changed in your system (even if you only changed one of them).

Then what you should do is

$('#usuario , #emailA').change(function() {
  // solo ejecutar si ambos input han sido modificados
  if (status_correo && status_usuario) {
    // realizar acciones
  }
});

Now, the order of events and their controllers is important. The event handlers will be executed in the same order in which they were associated. So it is key that the controller that you just modified is moved after the other two (so that the values of status_correo and status_usuario are updated before checking them).

With what in the end you should have something like this:

$('#usuario').change(function() {
  status_usuario = true;
  _sumbitForm();
});

$('#emailA').change(function() {
  status_correo = true;
  _sumbitForm();
});

$('#usuario , #emailA').change(function() {
  // solo ejecutar si ambos input han sido modificados
  if (status_correo && status_usuario) {
    // realizar acciones
  }
});

Here is a demo (with the contents of the simulated event handlers) showing how the last controller only executes when the two input have been modified:

var status_correo = false;
var status_usuario = false;

$('#usuario').change(function() {
  status_usuario = true;
  console.log("#usuario modificado");
});

$('#emailA').change(function() {
  status_correo = true;
  console.log("#email modificado");
});

$('#usuario , #emailA').change(function() {
  // solo ejecutar si ambos input han sido modificados
  if (status_correo && status_usuario) {
    console.log("ambos se modificaron! realizar acción conjunta");
  }
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

<select id="usuario">
  <option>Elige una opción</option>
  <option>Usuario A</option>
  <option>Usuario B</option>
  <option>Usuario C</option>
</select>

<select id="emailA">
  <option>Elige una email</option>
  <option>GMail</option>
  <option>Hotmail</option>
  <option>Yahoo!</option>
</select>