Hint, Virtual copies are simply "Virtual" they are not actual image files. The info about the virtual copies is stored in the Lightroom Catalog file.
When you select a virtual copy in Lightroom the original file is used by Lightroom and the info about the virtual copy from the Catalog is utilized to render and display the "VC".
Also be aware if you delete or remove the original file you will also loose all related "Virtual Copies"
You can get info and tutorials on line. See a related link below.
I know that , but since other metadata gets correctly update when I sync them I wonder why the time is not
Sync and Copy Metadata have never included the ability to copy capture time -- it seems like a strange omission to me. You could file a feature request in the official Adobe feedback forum: Photoshop Family Customer Community . (Adobe wants all product feedback posted there -- they rarely participate in this forum, which is primarily user-to-user.)