You may use tar on Android, Linux, Mac or Windows. As you like. The only difference is that Linux (and Mac) does deliver tar itself, for Android and Windows you may need a download.
If you don't like tar, you can try any other archiver that exists on all concerned OS, eg 7z or zip could be fine also.
The idea is that the archiver stores the date and restores it. This is a different, much more reliable approach than trying to copy timestamp. Especially for folders the file operations usually don't even try to restore the timestamp, the idea is that the folder is created when copying. Archivers mostly care about folder dates. Gnutar has quite some logic implemented to first copy all of the the files and afterwards set the timestamp for the folder, because adding a file to a folder sets a new timestamp.
This is the background why I recommended tar. It is the oldest tool, very reliable and exists nearly everywhere.