When an Internet-enabled disk image is downloaded by Safari (and Safari’s Open “safe” files after downloading preference is checked), it is automatically expanded into a folder and the disk image file is moved to the trash.
If the disk image has a background picture, it is not transferred to the expanded folder.
Note: DropDMG ignores this option when running on macOS 10.15 or later, as macOS no longer supports creating Internet-enabled disk images.
Note: Safari under macOS 10.7 and later does not honor the Internet-enabled setting, although there has been no indication from Apple that the feature has been removed.
Note: On macOS 10.2.2 through 10.2.8, this also happens whenever an Internet-enabled disk image is mounted (by any program). On earlier versions of macOS, Internet-enabled disk images are treated just like other disk images.