Can't find newly added playlist in iphone music app

I just applied to 3 month trial to check out if apple music is worth is, but unfortunately I am already facing some difficulties. I am having some problems with playlists. Either I don't fully understand the concept of apple playlists or they don't work as I expected. Hopefully somebody can help me with this.

Here it goes: When I go to iphone music app I see 5 tabs at the bottom of the app: Library, For You, Browse, Radio and Search.

- "Library" tab is obviously empty, as I am not planning on downloading and keeping any songs on my iphone at the moment

- "For You" tab has multiple sections Recently Played, Friday's Playlists, Friday's Albums, Artist Spotlight Playlists, New Releases and lastly Connect with Artists

- "Browse" tab has some featured playlists and other stuff

- "Radio" self explanatory

- "Search" as well.

So here is the problem whenever I pick up the song from "For You", Browse or Search tabs, select the song, then select 3 dots, and press add to playlist (new or some existing), there is a popup saying 1 song was added to your playlist.

The big question - Where do I find my playlists?

If I open my macbook and go to iTunes, I do see there all my playlists and newly added songs as they get synced over wifi. Both macbook and iphone are set to use iCloud Library if that makes any difference. However as I mention I can't see my custom playlists on my iphone, whether they were created from the mac or phone.

EDIT:

Never mind I did manage to get this thing to work. Basically you need to add a "stub" (at least one) song to your library so your library tab won't be empty. After adding at least 1 song to my library a playlists section appeared. Exactly what I was looking for. To be honest quite counter intuitive from apple side, but it is what it is.

Message was edited by: rob188221