Not so much a change - more a 'moving on'. The belonging and the giving are a continuum - part of the act of the will of the Father decided before creation began, but awaiting a certain time in history, after the Son had carried out his part in history to establish the legal basis to secure those he had been given, in the Father's will. Some might call that a progression. Others might disagree and think of different stages. That is likely if they think from the point of view of one of those disciples, and not from the point of view of the Father. To elaborate:
God's word is eternally secured in the heavens.
"For ever, O Lord, thy word is settled in heaven" (Psalm 119:89).
"So shall my word be that goeth forth out of my mouth: it shall not
return unto me void, but it shall accomplish that which I please, and
it shall prosper in the thing whereto I sent it" (Isaiah 55:11)
"I will praise thy name for thy lovingkindness and for thy truth: for
thou hast magnified thy word above all thy name" (Psalm 138:2).
Hindsight is a wonderful thing for the disciple who comes to understand the significance of God's choosing, and of Christ's presence. Perception is what changes with the disciple. But nothing has changed with God! And the only sense in which anything could be said to have changed in history is that, at Calvary, Christ secured the legal basis for claiming those whom God gave him from before creation began. The scope of this is so vast that in includes all people of faith from Genesis, through the whole of the Old and New Testaments, and right up till the time God's Day of Salvation closes, when the Day of Judgment starts.
Now, all of that was known in the Godhead before creation started. The Bible has abundant statements about that. So, if every single person whom God had chosen to be saved in Christ was decided upon before any humans came to exist and before the Son became the man, Jesus, and the Father and the Son also decided when those ones would be 'given' to Jesus, the position of those people never changes. What does change is that they find themselves alive at a certain point in time, and for those ones the truth of this scripture is experienced: "The entrance of thy words giveth light; it giveth understanding unto the simple" (Psalm 119:130).
But that word was already decreed in eternity past; it's just that the individuals concerned could not experience their position of security in God, through Christ's indwelling, until the Holy Spirit granted them understanding. Now the disciples come to know God's word, so they keep it; God's words begin to 'enter in' and they are aware of their transforming power. That is a manifested sign to any who care to look, that a person really is a disciple of Christ - they keep those precious words of truth.
Strange as it may sound, they were alive to God even before they existed, but at some point after they started to exist physically, he brought them to life spiritually. That's where the work of Christ and the Holy Spirit combine to bring those chosen ones to spiritual birth for the first time. At that point, they are adopted into God's family and they begin to grow, spiritually. Their understanding increases, along with their appreciation.
However, just as to worship Christ is to worship God, so to belong to Christ is to belong to God. There could not be a time when 'only' the Father could say those yet-to-exist humans were his, and his alone, and later he would let them belong to the Son too. Why not? Because orthodox Christian doctrine shows that the Son is the Eternal Son. To belong to the Father is to belong to the Son, and vice versa. The Son was never created - he is the only-begotten, which does not mean a starting point in time, but shows his unique relationship with the Father.
It seems to me that the fundamental change once a person discovers that they now belong to the Son by faith, is that they should also discover that they likewise belong to the Father, and this constitutes the 'oneness' prayed about in John chapter 17.
From God's point-of-view, nothing has changed; that which was decreed has come to pass, with each individual concerned. But from the individual's point-of-view, everything has changed! And the change starts with their new-found relationship in belonging to Christ, which then grows to appreciating how that means they also belong to God. Yet, because in John chapter 17 we learn that the Father and the Son are 'one' in the same sense that they will bring the disciples into that one-ness of unity, the position of those who become disciples is as fixed (secure) at the decree - the word - of God before creation began, as it will be for their entire duration on earth.