Hi,
these files are created as http server user and have rights of that user. You can delete it using root account or with this user. After you moved epesi to another directory, and your configuration is not simplest one, epesi uses config.php variable EPESI_DIR. If you don't have defined this variable, your server configuration is simple and epesi detects it automatically.
We know that minify data directory grows fast, because it caches all possible css/js files, compressed versions and normal ones, some of combinations... to serve one file instead of couple of css'es at once.... etc After one year of usage my cache directory is 15MB. Minify cache is recreated so you can purge it from time to time.
Paul