How to get notified when somebody tweets on Twitter?

I have an iPod Touch 4G, and I want to be notified when One Direction/other tweets. There's a way to do it if you have an iPhone, like it'll text you when their tweet. And I know there's a way you can do it with an iPod Touch too, where instead of it sending a text to you, it will pop up on your screen, like when somebody tweets you.

I would think that if you connect to twitter via the twitter app, then it should send you a notification whenever someone tweets you.

Not really sure what you mean but when you subscribe to someone's tweets like One Direction, it comes to your phone as a text like you said, another thing is make sure you have the app downloaded and not just open it in your internet, But I think they can only send as text messages like it may not pop up on your screen like you want it, not really sure but you can always just play around with your twitter settings. Hope I helped.