Wife and daughter went on a long trip so I had to dump a ton of recordings onto my tablet recent. Very familiar with this option. If your device has an SD card then in the app's settings under Transfers you will see the two areas (have a Samsung tablet and phone so I have the external card option which is great). One for internal and one for external storage. You have the ability to turn external on or off from there.
One thing to note. Not sure if it was just me or if a bug on the Dish app, but at times I would set a DVR recording to transfer to my tablet and even though I did have the external card option enabled the recording would transfer to my internal storage. I had to cancel the transfer, go to settings, disable then enable the external storage option then try again. Frustrating.
And you will not be able to see individual recordings on your device IF they are stored on internal memory. Believe the app bundles the recordings into the application somehow where you do not see the individual transfer files.