I don't know any hard facts about it.
Let's say I have an hour drive and I have solid LTE for the first 10 minutes. I put on an album when I start driving. In that time it will start caching songs that will be played next so if service goes away it doesn't stop playing music.. Even though I haven't saved any of those songs for offline playing.
A couple things to note:
I cannot skip songs if my iPhone says "no service." I cannot chose a different song or anything else. But it will always continue playing as long as there is music in a que. If I have so much as 1 bar of 4G (which isn't enough to send a text usually) then I can skip and whatever else. Also, say I have a song that I haven't played today but a few times in the recent past, I can play that song (and many like it) instantly without waiting on it to buffer when I have that low 4G. Likewise, if I have a song that's been in my library for a while but I haven't played it in a month or two, it will require a buffer period(with low signal) and usually won't play.
This would mean that Apple Music saves a certain amount of music (assuming your storage isn't full) to the hard drive in the phone with out telling you.
Like I said, the actually workings of this may differ, but this is what I experience.
Does this answer your question?