My understanding is DoubleTwist is intended to sync iTunes content with an Android phone. It is not (as far as I know) a general purpose file transfer tool. In any event, I don’t see how merely having DoubleTwist on one’s Android phone would allow a Mac to mount it as a USB drive.
There is a free companion syncing app for the Mac here: https://www.doubletwist.com/desktop. When I search on the term USB at DoubleTwist’s website, all of the returned articles are for Windows and/or Android. It’s unclear to me a USB connection is an option with a Mac though it may be.
I use a competing app to sync iTunes content with Android devices:
It works with USB (I prefer using WiFi) but, again, isn’t intended to be a general purpose file transfer tool. For that, Google’s Android File Transfer probably is the best solution. If wanting to move photos from your Android device to Photos or iPhoto (which you have depends upon age of one’s Mac), then changing the USB connection method on the phone to a “camera” is an option.