You are talking about the doctrine of "Federal Headship." Adam and Eve's eyes being opened is the "effect" and not the "cause"; Which is a different thing. Eve still sinned in eating of the wrong tree. However, Adam is the "federal head" of the entire human race; And sin is passed down by the male seed. Hence, why Jesus had to be born of a female virgin supernaturally. But when Adam seen that the fruit looked good to eat (lust), he bit of the fruit and sin took place (with his action), and then the result was spiritual death whereby both of their eyes were opened (Because Adam is the Federal Head of the entire human race).
In other words, first there is lust (Which is bad), that is then followed by sin (Which is bad), that then results in death (Which is bad).
James 1:15
"Then when lust hath conceived, it bringeth forth sin: and sin, when it is finished, bringeth forth death."
In other words, in order for me to be tempted by something, I need to have a desire (or lust) for that thing on some level for me to actually be tempted. If there is no actual desire (lust) in a particular form of temptation put upon me, then there is no real temptation involved.
I mean seriously, if Jesus was tempted in all points like us (As you suggest), then that means you are saying that Jesus struggled to not to look at women in the wrong way. That means that there was some kind of wrong desire (or lust) in Him in order for Him to struggle in trying to refuse in not wanting to look at women the wrong way. But Jesus said if you lust after a woman, you have committed adultery already in your heart. See, that is why he was never tempted in the way that you think.
Jesus was ONLY tempted in all points like us by the fact that He had limited knowledge (While in the flesh of a man during His Earthly ministry). But Jesus never desired or lusted in doing bad. Such a thing would have brought forth sin; And there is no stage before lusting. You either have a desire to do good or you don't. Jesus' desire was always to do good. Always 100% of the time because He was the Word made flesh.