Bypassing paused internet access

It’s very frustrating when I’ve paused my children’s devices to limit phone use and then I see them still able to access the internet. How is this happening and what can be done to stop it and prevent it from happening in the future? I understand kids are gonna push limits but with technological advancements, establishing rules and enforcing consequences these days puts parents between a rock and a hard wall. There is no form of censorship anymore. So please help us have a way to protect our children from themselves and find a solution to this issue. 

Thanks