The corruption of Ea was due to the Music. It was sung wrong, therefore evil was woven into the very fabrics of Ea.
From "Of the Beginning of Days"
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Therefore he(Eru) willed that the hearts of Men should seek beyond the world and should find no rest therein; but they should have a virtue to shape their life, amid the powers and chances of the world, beyond the Music of the Ainur, which is as fate to all things else; and of their operation everything should be, in form and deed, completed, and the world fulfilled unto the last and smallest.
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Melkor's fall was not a result of the Music. Therefore, I'd say that Melkor's reason for being evil is not the same reason that some of the creatures of Middle-earth would be evil.
I believe Melkor became evil because he fell to the temptation of the creator. He believed that what he created was his to control. He forgot that everything belonged to Eru. Because of this error, he longed to control what he had no right to control. He rejected Eru's way for his own, thereby becoming evil.