Some questions about using iTunes Match

I recently bought an iTunes Match subscription and added all my music from my computer into the cloud. I'm using iTunes Match so I can listen to my music at work and have a larger variety.

Once I turned on iTunes Match on my phone, I noticed I was getting message for my storage being full. I went to manage storage and I have over 1 gb of music so it looks like iTunes Match downloaded all my music to my phone. I have a couple questions about this.

1. Is itunes match supposed to download all songs to my phone- is this the purpose of it?
2. Is it possible to have all the music in the cloud and just download the songs I want to my phone? If so, how do I do this without downloading everything?

I've tried deleting my music through Storage in Settings but my phone will always re-download it at some point. I have even tried turning off itunes match and my phone continues to download any music I have in the cloud. I'm worried that I'm using a lot of my data because of all this downloading.

Maybe I didn't fully understand the info about itunes match- but I thought the music was stored in the cloud and I could stream it without downloading it to my phone. My understanding was itunes match gave me the ability to have access to my entire music collection that is saved in the cloud without taking up extra space on my phone.

Any insight would be very helpful, thanks!