I find Apple's music app on iOS terribly hard to use. It didn't used to be this way. I struggle to do basic things, like just playing the songs in order on an album! Sounds silly, but there are so many buttons that sweep away to different screens, and it's not at all clear what you are doing.
Now I just use GoodReader to store and play back all offline albums, since it's just a file directory and I can just play the tracks in the order they are stored.
When you're looking at an album in Music, there's a play button right above the song list that will play it in order and should disable any previously enabled shuffle mode. It just goes off of whatever iTunes metadata is setup, so if that is correct, it'll play in order.
Now I just use GoodReader to store and play back all offline albums, since it's just a file directory and I can just play the tracks in the order they are stored.