Outlook SSL Security Alert Certificate Name is Invalid

Our Exchange Certificate expired and we had to renew the SSL. after deploying the new SSL, some users started getting SSL security Alert on their outlook’s

No all users but some, after seeing the screenshot we narrowed it down to that the SSL is ok but the Security alert is about One of the DAG Server Name not included into the SSL. so I knew that this has to do with Autodiscover URL.
I logged into Exchange Server and executed the following command
Get-ClientAccessService -Identity EX04SERVER | Select AutodiscoverServiceInternalUri
Output I received was as below

AutoDiscoverServiceInternalUri
------------------------------
https://EX04SERVER.my.localADdomain.com/Autodiscover/Autodiscover.xml
This clarifies that the Autodiscover is accessing internal Server name URL therefore it had to be changed to Global URL
Executed following command
Set-ClientAccessService -Identity EX04SERVER -AutoDiscoverServiceInternalUri
https://mail.mymaildomain.com/Autodiscover/Autodiscover.xml

and the issues is no longer reported by any users
Here in this scenario
My server name is : EX04SERVER
My external mail domin is : mail.mymaildomain.com
My SSL certificate name is : mail.mymaildomain.com
My Activedirectory Domain is: my.localADdomain.com