"Just don't" is often used as a response to the question (or some variation of) "Why not?":

>Dad: Don't touch that
>
>Kid: Why not?
>
>Dad: Just don't.

In your example, they're shutting down the question "Why can't I disturb you?", "What are you doing?", etc.. before you have the chance to ask it, implying they are *expecting* you to ask it.

>Dad: Don't touch that
>
>Kid: -
>
>Dad: Just don't.

It's quite common, so much so that it has made it's way into one-way conversation for comedic effect, hence the t-shirt print.