Alaska---Just because death of our bodies occurs, this does not mean that a second death to our souls has to be immediately at the same time.
16 And the LORD God commanded the man, saying, Of every tree of the garden thou mayest freely eat:
17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.
Eating of it in itself was a sin but notice what the tree was.
Before eating of this tree the knowledge of good and evil was not part of their reality. Simultaneous sentence of death for eating along with this knowledge that would only exacerbate this situation of their entering into sin and guilt.
Paul refers to this state experienced by all of mankind of sin having connection to knowledge through a fallen nature:
7 What shall we say then? Is the law sin? God forbid. Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet.
8 But sin, taking occasion by the commandment, wrought in me all manner of concupiscence. For without the law sin was dead.
9 For I was alive without the law once: but when the commandment came, sin revived, and I died.
10 And the commandment, which was ordained to life, I found to be unto death.
11 For sin, taking occasion by the commandment, deceived me, and by it slew me.
12 Wherefore the law is holy, and the commandment holy, and just, and good.
13 Was then that which is good made death unto me? God forbid. But sin, that it might appear sin, working death in me by that which is good; that sin by the commandment might become exceeding sinful.
14 For we know that the law is spiritual: but I am carnal, sold under sin.
15 For that which I do I allow not: for what I would, that do I not; but what I hate, that do I.
16 If then I do that which I would not, I consent unto the law that it is good.
17 Now then it is no more I that do it, but sin that dwelleth in me.
Since he is using 'thou shalt not covet' as his example, he is referring to law as pertaining to human conscience, in other words the basic knowledge of right and wrong (good and evil) inherited from Adam.
Receiving the knowledge of good and evil insured the continuation of sinfulness because they began to experience this new sinful nature as a result of receiving it. They in the garden had not been created to deal with "right and wrong" "good and evil". Hence their and our failures in that area and hence all have sinned and the wages of sin is death.
The payment, is a price, is a ransom. It has been payed for us so that we can now deal with right and wrong and not fail anymore but by walking in the Spirit, that "concupiscence" or fleshly nature to sin would no longer express itself to the extent of us committing sin. Not to say we will not be tempted like even Jesus was, but he did not yield and commit sin like his body now is also supposed to be not yielding and not sinning.
4 Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine: the soul that sinneth, it shall die.
The NT reveals the prospect of eternal life not clearly revealed before. Likewise the reality of two deaths. The flesh and the soul.
28 And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.
This death of the soul is apparently designated to be performed at a time at the very end. So even those who have passed on way back at the beginning of time may be waiting in sleep (death) until they are awoken for the big gathering of the goats on the left and the sheep on the right.