Cellular Data & GroupMe

Yesterday, I turned off cellular data for all of my apps (to test wasted data usage). There's minimal, so I'm not worried about it. I went home and was on wifi, no issues there. Coming to work this morning (no wifi available), I suddenly get 8 new GroupMe messages pop up on my screen. I open the app and the messages are not visible, and the Apple message on the screen says "Cellular data is turned off..." - you know that screen. Any who... checking the Notifications drop down, they are not listed there, and I can't find the 8 message. So I turned cellular back on for GroupMe, and the 8 messages are now present.

Ok, getting to my question... Why did I get notifications this morning of 8 new messages when my settings for cellular usage was turned off? Are Notifications and Cellular two completely different things I need to be turning off, or shouldn't Cellular dominate all other settings regarding data usage?

iPhone SE Version 9.3.4 (Don't tell me an update will fix this!! I hate that answer!)

Thanks in advance!!