Well your line of code (involving Aspose.Cells API with some older version (v4.7.1.x), i.e.., "workbook.Save("Report" + DateTime.Now.ToString("ddMMyyyyhhmmtt") + ".xlsx", FileFormatType.Excel2007Xlsx, SaveType.OpenInExcel, HttpContext.Current.Response);" is equal to the following lines of code without involving Aspose.Cells APIs to response the file on the client side:
MemoryStream tempStream = new MemoryStream();
//You may change it accordingly if you are saving in XLS file format
Response.ContentType = "application/vnd.openxmlformats-officedocument.spreadsheetml.sheet";
Response.AppendHeader("Content-Disposition", "attachment; filename=" + workbook.FileName);
You may confirm it and use the above lines without involving Aspose.Cells's APIs to response the file on the client side and you will see the same behavior, so it is the behavior of Response Object.
If you feel the lines in bold (above) have different behavior than "workbook.Save()"
let us know.