Trying to get my head around mineralize and when the N will be available.

So I work my last year corn crop in last fall, not very well, older disc, but got it cut up some and saw a little black dirt.  OK, now the soil is mineralizing that old residue.  People say it takes N to break down the carbon (old stalks) and then the N will be available again to the crop.  If I am right here, when will the N be available ?  This year's crop or next year ?

Same with planting rye in the fall to capture left over N and other nutrients, keeping them from leaching.  Let rye grow some in the spring, kill when it is knee high or a little more.  Now the rye (carbon) needs to be broken down before those nutrients can be available to the crop.  I would think those nutrients would have to be available to this years crops or what was the point in planting the rye. Yes?  How much credit of N do you give to the killed rye ?