Per se causes bring out the effect
through themselves.
Per accidens causes are merely conjoined with the
per se cause. So the the wisdom of Aristotle does not directly cause him to be hungry. It can only be an
accidental cause of his hunger insofar as it for example makes him use his brain more.
This is from Physics book 2:
That which is per se cause of the effect is determinate, but the incidental cause is indeterminable, for the possible attributes of an individual are innumerable.
I can make an argument that
per se causes can't possibly be identical with the effect (I thought it's obvious but ok):
First of all, it's a title of a chapter in Physics VII: "It is necessary that whatever is moved, be moved by another." Another is not identical. Unless you say that Aristotle says that beside the immediate mover there is yer another cause of an effect which is identical with the effect.
Second Aristotle admits chains of
per se causes. Multiple things can't be identical. The prime mover is a
per se cause of all movement. Are you to suggest that the prime mover is identical to every movement? That would be ridiculous in Aristotle.
Also the amount of people with their own completely ignorant interpretation is saddening. It's not you, you make sense and the essential/simultaenous distinction is subtle and it's a wide problem in the litterature). The definition you quoted concerns Scotus, not all scholastics definitely. Aquinas and Suarez wouldn't agree. And they're taken to be the orthodox Aristotellians, Scotus' doctrines are controversially Aristotellian.
As to the non--simultaneity of immediate cause and effect - ok I just found a passage in Aquinas' commentary to Posterior Analytics touching just on this issue:
But although the motion has succession in its parts, it is nevertheless simultaneous with its movent cause. For the moveable object is moved at the same time that the mover acts, inasmuch as motion is nothing else than the act existing in the moveable object from the mover, such that in virtue of that act the mover is said to move and the object is said to be moved. Indeed, the requirement that the cause be simultaneous with what is caused must be fulfilled even more in things that are outside of motion whether we take something outside of motion to mean the terminus of the motion-as the illumination of air is simultaneous with the rising of the sun--or in the sense of something absolutely immovable, or in the sense of essential causes which are the cause of a thing’s being.
It seems you're right - an immediate mover must be simultaneous with the actualization. But it's not identical. Also there are
per se causes which are not simultaneous with the effect. (consider a transformation of an element, an efficient cause ceases to be once the effect is in actuality).