Well here’s a couple ways why the charismatic movement was inspired by the Holy spirit and the Second Vatican Council. Bl. Pope John XXIII started the council with the intention of igniting a new Pentecost in the church. The prayer he had promulgated just before the council was a prayer to the Holy Spirit asking “renew in your Church your miracles as of a second Pentecost”. Then during the actual Council, it reaffirmed the importance of the charismatic dimension.
According to Bl. Pope John Paul II:
"4. With the Second Vatican Council, the Comforter recently gave the Church, which according to the Fathers is the place “where the Spirit flourishes” (Catechism of the Catholic Church, n. 749), a renewed Pentecost, instilling a new and unforeseen dynamism.
Whenever the Spirit intervenes, he leaves people astonished. He brings about events of amazing newness; he radically changes persons and history. This was the unforgettable experience of the Second Vatican Ecumenical Council during which, under the guidance of the same Spirit, the Church rediscovered the charismatic dimension as one of her constitutive elements: “It is not only through the sacraments and the ministrations of the Church that the Holy Spirit makes holy the people, leads them and enriches them with his virtues. Allotting his gifts according as he wills (cf. 1 Cor 12:11), he also distributes special graces among the faithful of every rank… He makes them fit and ready to undertake various tasks and offices for the renewal and building up of the Church” (Lumen gentium, n.12).
The institutional and charismatic aspects are co-essential as it were to the Church’s constitution. They contribute, although differently, to the life, renewal and sanctification of God’s People. It is from this providential rediscovery of the Church’s charismatic dimension that, before and after the Council, a remarkable pattern of growth has been established for ecclesial movements and new communities."
vatican.va/holy_father/john_paul_ii/speeches/1998/may/documents/hf_jp-ii_spe_19980530_riflessioni_en.html
During the council, there was an intervention made by one of the key leaders (Cardinal Suenens) to insert something about the charisms (see Lumen gentium 12). It is crucial to understand that the cardinals and bishops, in their discussion about charisms (specifically those gifts mentioned in 1 Corinthinas 12) we responding to pure grace! This was several years before any real charismatic renewal kicked off in the Church!