Where did people who lived in Jesus's time go to when they died? This sounds weird but when Jesus existed between approx. 6-3 BCE to 33 CE in Judea as a man (still retained His God nature) how were people living in this exact time frame judged after they died? 


Did Jesus judge them, even as a man on Earth? I'm aware that He did
cast out demons and presumably sent them to hell during His exorcisms
and I'm wondering if this extended to the souls of wicked humans
Did His "God nature" perform the executions?
Or did God the Father (or possibly the Holy Spirit) do the job?


I seek an answer preferrably from a mainstream/orthodox (NOT Eastern Orthodox Christianity) Christian perspective.
As a Christian of the Reformed Protestant persuasion, I do not think there is anything in the New Testament to suggest that Jesus, when on earth, was personally or individually in the business of judging the dead, either Jew or Gentile, or of escorting them either to heaven or to hell.  We know that our eternal destination is decided at the point of death.  The basis of judgment is on how we lived our lives.  Daniel spoke of the Book of Life and so does Revelation, in which names are written.

Ecclesiastes 12:6-7 informs us that we must remember God “before the silver cord is severed, or the golden bowl is broken; before the pitcher is shattered at the spring, or the wheel broken at the well, and the dust returns to the ground it came from, and the spirit returns to God who gave it.”
Significantly, verse 14 says “God will bring every deed into judgment, including every hidden thing, whether it is good or evil.”

So it is God who does the judging.  Just because the third person of the Triune Godhead was temporarily on earth does not infer that the Father and the Holy Spirit were incapacitated in any way!
However, Jesus did have something to say about the condition of the dead and WHERE the soul went while awaiting the resurrection and the judgment to come.  It’s in Luke 16:19-31:

There was a rich man who was clothed in purple and fine linen and who feasted sumptuously every day.  And at his gate was laid a poor man named Lazarus, covered with sores, who desired to be fed with what fell from the rich man’s table.   Moreover, even the dogs came and licked his sores.  The poor man died and was carried by the angels to Abraham’s side [or bosom]. The rich man also died and was buried, and in Hades, being in torment, he lifted up his eyes and saw Abraham far off and Lazarus at his side.  And he called out, ‘Father Abraham, have mercy on me, and send Lazarus to dip the end of his finger in water and cool my tongue, for I am in anguish in this flame.’  But Abraham said, ‘Child, remember that you in your lifetime received your good things, and Lazarus in like manner bad things; but now he is comforted here, and you are in anguish.  And besides all this, between us and you a great chasm has been fixed, in order that those who would pass from here to you may not be able, and none may cross from there to us.’  And he said, ‘Then I beg you, father, to send him to my father’s house—for I have five brothers—so that he may warn them, lest they also come into this place of torment.’  But Abraham said, ‘They have Moses and the Prophets; let them hear them.’  And he said, ‘No, father Abraham, but if someone goes to them from the dead, they will repent.’  He said to him, ‘If they do not hear Moses and the Prophets, neither will they be convinced if someone should rise from the dead.’  (English Standard Version)

The Greek word ‘kolpos’ is variously translated as “Abraham’s side” (NIV, ESV), “next to Abraham” (CEV), “with Abraham” (NLT), “the arms of Abraham” (NCV) and “Abraham’s bosom” (KJV).
“Abraham’s bosom” was used in the Talmud as a synonym for heaven.  The image in the story is of Lazarus reclining at a table leaning on Abraham’s breast at the heavenly banquet.  The point of the story is that wicked men will see the righteous in a happy state, while they themselves are in torment, and that a “great gulf” that can never be spanned exists between them (Luke 16:26).  Until the resurrection, the souls of those who have died are in an “interim holding place” – either in a state of bliss (paradise, or Abraham’s bosom) or in a state of torment.
It was at the cross that God pronounced judgment on the unbelieving world and on the enemy of our souls, Satan.  Jesus said, shortly before His arrest, “Now is the time for judgment on this world; now the prince of this world will be driven out” (John 12:31).  However, there are future judgments to come:

The judgments of the tribulation period (Revelation 6—16)
The judgment seat of Christ (2 Corinthians 5:10)
The judgment of the nations (Matthew 25:31–46)
The judgment of angels (1 Corinthians 6:2–3)
The Great White Throne Judgment (Revelation 20:11–15)

This final judgment of unbelievers occurs at the end of the Millennium, before the creation of the new heaven and earth.  At this judgment, unbelievers from all the ages are judged for their sins and consigned to the lake of fire (the permanent condition of those who reject Christ).
So, who judged all those persons who died while Jesus was on earth?  The Bible does not say, and I’m not about to guess.  It’s an interesting question but I suspect that the Father and the Holy Spirit had everything under their control (including sustaining the universe and all life) while the Logos, the Word of God, was on assignment for those few, short years when he dwelt with us.