iPhone/iPad: How to add files with the iOS Files app

Open the Files app
Open the folder containing your music, and tap "Select"
Select the files you want to import into Doppler
At the bottom of the screen, tap the copy button
Select the Doppler folder
Tap "Copy" and re-open Doppler
From your iPhone/iPad, re-open Doppler and select the "Settings" tab along the bottom of the screen
Select "Manage Library" and then select "Update Library" and wait for the progress indicator to disappear