Data is turned off, but i still get notifications?

I have an iphone 5c. The main data switch is turned on, but for apps that use a huge amount of data like snapchat, facebook, and instagram, I have data switched off. Yet I still receive notifications for these apps? Ill get the facebook notification on my lockscreen, and then go to the app, and it says it can't load. I want to know how this is possible and how I can make it stop. I don't want to completely shut off push notifications, because sometimes I do want those apps to be on data, but most of the time I don't. Why aren't they completely disconnecting when I have data turned off for them?

Settings > notifications > click on the app you want and tap. Your phone isn't going to magically know when you want the notifications off for these apps, so you have to do it yourself.

Push notifications don't rely in a data connection. Pure and simple.

I'm just curious, are you by chance connected to Wi-Fi when this happens? Usually turning data off only turns off mobile data. If your on a Wi-Fi then it will connect to the internet and function as it would if your mobile data was on.