To be sure we are on the same page, the process is as follows:
A downloaded application is provided as a disk image file which includes a .dmg extension. When double-clicking on the downloaded .dmg file, the disk image is mounted on the Desktop.
To install an application from a mounted disk image that is provided as a bundle without an installer, you drag the application's icon from the mounted disk image to your Applications folder which copies the application to the hard drive.
To unmount the disk image from the Desktop when finished, you can click and drag the mounted disk image to the Trash can in the dock or select the mounted disk image and at the Finder menu bar, go to File and select Eject.
After the disk image is unmounted from the hard drive, you can delete the downloaded .dmg file.