Why does my data usage go up when I'm not even on it?

And if I get a twitter notification while I'm off of Wi-Fi, does that take up data? Btw I'm not opening twitter, I'm just getting a notification.

You will be charged as long as you are connected to the cellular data, no matter what you do. So, disable cellular data when you are not using it and save your balanced.

No only if you go in

Yup definitely

The second you get anything on your phone. Any alert (other than emergencies and stuff), any preview on your lock screen, a ding from a text in your inbox, it's using data. You don't have to be on it, the fact you have it, means it's using it. Best luck.