I recommend when you are adding the required status via Javascript - to set both the required attribute and adding a class to help identify them.

$('.myCSSClassName input').attr('required', 'true');
$('.myCSSClassName input').addClass('required');

By the way, that doesn't add the asterisk ( * ) to the field.  But this is a way to do it:

$('.myCSSClassName input').closest('li').find('.cf-label').find('span').find('span').first().append('<span class="cf-required">*</span>');

Take that a step further - assume I want to remove that field requirement upon form Reject, but keep it in place for Approve or Submit (allow a form to be rejected even if it is missing required fields).  I can do this kind of code - it makes the field required, but removes the requirement when you click Reject: 

$(document).ready(function () {

  $('.myCSSClassName input').attr('required', 'true');
  $('.myCSSClassName input').addClass('required');
  $('.myCSSClassName input').closest('li').find('.cf-label').find('span').find('span').first().append('<span class="cf-required">*</span>');
  
  
  //run these steps upon form reject (ignore required fields and also ignore pattern matching).
  $('.action-btn.Reject').on('click', function() {
    //since we added the "required" class name to the field's input, we can
    //run the following code on just the required class - if we wanted this
    //to work on a field that was set to Required in the Layout screen 
    //instead of via the code above, we'd need to reference the class name 
    //and input at this point (i.e. $('.myCSSClassName input').each...) since
    //class names set via the Layout screen are applied to the whole field
    //not just the input part of the field.
    $('.required').each(function() {    
	  $(this).removeAttr('required');
      $(this).removeClass('required'); 
    });
  }); //end of $(".action-btn.Reject").on('click', function() {
	
}); //end of $(document).ready(function () {

(Be sure to disable back-end validation if you are doing this, or you may get an error).

Now, that doesn't exactly answer your question, but I think it is related.  To address your question more specifically, we can look at Submit or Approve buttons by using $('.action-btn.Approve') or $('.action-btn.Submit') instead of $('.action-btn.Reject').  Within that code, if we want to force it to validate before completing the Submit or Approve actions, we can trigger the code: $('#form1').parsley().validate();   Here's a sample: 

//run these steps upon form Approval (if all required fields are complete).
$('.action-btn.Approve').on('click', function() {
  var noErrors = true; 
  $('#form1').parsley().validate();
  $('.parsley-error').each(function() {
    noErrors = false; 
  });
  if (noErrors) { 
    //
    // Code goes here to occur just before form successfully submits (i.e.
    // add notes to a field, 
    // save the username of the submitter to a field, etc.)
    //
  }
  else { 
    //
    // Code goes here to occur if form failed validation.
    // 
  }
}); //end of $(".action-btn.Approve").on('click', function() {