Offline listening

[somnomania]

Plan: Premium

Country: USA

Android: 13

Phone: moto g play

Question: With downloading playlists for offline listening, is there any way besides waiting and then testing to know if it's actually downloading? There's no indicator (at least on mobile) that tapping the download button does anything, and a couple of days ago I was in the car listening to one I'd tried to download and the last three or four songs were missing (I'd told it to download and then it was likely HOURS before the wifi got turned off). Does the app have to remain open for it to download properly? Spotify's own help article about offline listening says there should be a green arrow next to things that have downloaded; I've never seen that icon, and yet some things are downloaded.