Egnyte Unified FTP service provides the ability to preserve timestamps when files are uploaded to the cloud from your computer. You need to enable the option to preserve timestamps in your FTP client. Note that not all FTP clients support this functionality in a standard compliant manner.
In Filezilla for example, the option to preserve timestamps is available in the Transfer menu as shown below. Once you select this option, uploaded files will be loaded into Egnyte with the original timestamp from your computer.