User is offline in omni-channel but still being assigned case. Any investigation steps can be troubleshoot such problem? Thanks!

We going to use Salesforce cloud service to handle our email cases.
Email from SmarTone customer to our service mail address, e.g. customer@smartone.com (mailto:customer@smartone.com) will be forwarded from our Exchange server to SFDC service cloud.
At last, SFDC service cloud will reply the customer mail directly by replying mail sent from your cloud.
 
It is found that customer will see a mail with “mail from” like below.
And it is not a simple email address, e.g. customer@smartone.com (mailto:customer@smartone.com)
 
This machine like presentation will make our customer confused.
It is NOT accepted by our Customer Service related departments.
 
Please help provide us the solution
 

Can we replace the following code:
redirectPage = new PageReference(String.format('/p/process/Submit?retURL=%2F{0}&id={0}', new String[] {sObjId}));

with:

Approval.ProcessSubmitRequest approvalRequest = new Approval.ProcessSubmitRequest();

approvalRequest.setObjectId(sObjId);

Approval.ProcessResult approvalResult = Approval.process(approvalRequest);

if (!approvalResult.isSuccess())
{
ApexPages.Message error = new ApexPages.Message(ApexPages.Severity.ERROR, 'There was an error with the Submit For Approval Request.');
ApexPages.addMessage(error);
}
redirectPage =new PageReference(String.format('/{0}', new String[] {sObjId}));
redirectPage.setRedirect(true);

}