[SalesForce] Values are not updated in Lightning after record update

You will have to assign the accList back to the aura:attribute after pushing elements.

var accList=component.get('v.AccountList');
    accList.push(0);//you are updating the local instance of the list, not the actual attribute.
component.set('v.AccountList', accList);//updating the aura:attribute.

I finally figured this out. This is actually a known issue between VF and background Apex changes (thanks Salesforce), along with navigation back to a Standard Page via PageReference:

https://success.salesforce.com/issues_view?id=a1p3A0000001C8QQAU&title=data-not-updated-in-ui-after-an-apex-update-in-lightning-experience

I found this Post that explained how to use remoting to force the refresh (in Lightning):

https://www.sales4k.com/sfdc/salesforce-lightning-refresh/

Unfortunately, that also did NOT (or no longer does) work either. It did however lead me to Googling caching issues with sforce.one.navigateToSObject in Lightning, where I found a Post that said sforce.one.back(true) does work in Lighting. Finally, I got it to work, using this approach. The following example illustrates my final solution:

Visual Force .page file:

<apex:page controller="YOUR_CONTROLLER" action="{!Launch}" cache="false" 
 lightningstylesheets="true">

   <script src="/soap/ajax/38.0/connection.js" type="text/javascript"></script>
   <script src="/soap/ajax/38.0/apex.js" type="text/javascript"></script>
   <script type="text/javascript">

      // Back NAV.Refreshed
      sforce.one.back(true); // While sforce.one.navigateToSObject(YOUR_ID) did NOT 
                             // refresh, sforce.one.back(true) did refresh

    </script>
</apex:page>

Apex Controller

global class YOUR_CONTROLLER  
{   
   public void Launch()
   {
      // Your update logic goes here (will properly refresh on backward navigation)
      ...
   }
}