Is it correct to say:
I need those reports, and I need them yesterday.
Shouldn't it be:
I needed those reports yesterday.
Or is this aberrant usage style simply a colloquialism?
This usage of yesterday is idiomatic, it's basically a synonym for "as soon as possible".
It means, "Today isn't really soon enough." (If I could, I would turn back the clock to yesterday to have those reports delivered.)