I am not sure I understand you correctly.
"Transferring an app" in our lingo means that you export an app in one system and then import it in another. It sounds like this is what you are doing from your description but it does not make sense in context. "Transferring apps" does not transfer any data or files - just application structure (we call that the app schema). In the target system you would not have any files or thumbnails from the source system. To achieve this, you would need to export and then reimport the actual data - doing this is possible, but not via application transfers.
If you migrate a whole instance (eg. the entire DB + state), you would also migrate files + thumbnails. But this is only relevant, if you want to move the entire r3 system.
