Multiple submits form and Ajax: Select which submit button is triggered
My solution was to remove the Drupal click event:

'event' =&gt; 'click',


And to manually add it via jQuery by finding the next input button:

$('input.form-text', context).once('field_validation_keydown').keydown(function(event) {
  if (event.which == 13) {
    $(this).parent().nextAll('input.ajax-processed').trigger('mousedown');
  }
});


But if anyone has a better solution, I'm curious to know about it.