It was like that for me too, and not for playlist, but for an album.
It's a really stupid "feature" if it is a feature. I have nothing against hearing similar songs right after i have finished an album, so i don't have to manually start something new. but when i have finished that album 3 days ago and i want to listen to it again, and I press play on this specific album it is RETARDED to start playing completely different songs. then we have a problem.
i went to web player on my PC and manually had to start the first song of that album to "restart" it.
I'm still listening on the web player, i have no idea if that "fix" will consist once i return to listening on my phone.
I was having this problem and just figured out why. Even though my playlist has a lot of songs AND autoplay is OFF, it was still happening. Finally I realized that many of my songs were "local files." They had an arrow next to them in my laptop playlist. None of the local files were showing up on the playlist on my phone (although, as an aside, I do have them locally on my phone). However, I deleted each local file on my playlist and replaced it with a Spotify version of the song. That finally fixed it. Now the songs appear on my phone's playlist and Spotify is no longer adding songs.