あなたって人(ひと)は、「やるな」と言(い)ったそばからやるんだから。
People like you are just… As soon as I told you not to do it, you still do it…
while そばから is slightly old fashioned, 言ったそばから is still common expression. 言ったそばから is much more common than 言うそばから. In this case, あなたって人は expresses exasperation of the speaker, similar to English "How dare you".