Is there A way to download tiles of the Tiff from the cloud processed projects?
Depending on which tiles you are referring to:
If you are referring to orthomosaic tiles, the one that you would obtain after desktop processing, then yes. To download them you will have to export the project to desktop from cloud.
On the other hand, if you are referring to the tiles that we are using to display the orthomosaic in the cloud then no.