What information do we have on the real vision of Pope Leo XIII?

An appendix of Vatican exorcist Fr. Gabriele Amorth's An Exorcist Tells His Story (pp. 37-40) cites:

1. Fr. Domenico Pechenino, Ephemerides Liturgicæ (1955), pp. 58-59.
2. Card. Nasalli Rocca, pastoral letter for Lent, Bologna, 1946.
3. Pope Pius XI, reproduced in Civiltà Cattolica, 1930, vol. III.

The translation of the entire appendix below is based on the Italian version, Un esorcista racconta:

The diabolic vision of Leo XIII

Many of us remember how, before the liturgical reform due to the Second Vatican Council, the celebrant and the faithful knelt at the end of each Mass to recite the prayer to Our Lady and one to St. Michael the Archangel. We report the text of this latter because it is a beautiful prayer which can be fruitfully recited by all:

Saint Michael the Archangel, defend us in battle. Be our protection against the wickedness and snares of the devil. May God rebuke him, we humbly pray. Do Thou, O Prince of the Heavenly Host, by the Divine Power of God, cast into hell Satan and all the evil spirits who roam throughout the world seeking the ruin of souls.

How did this prayer come about? I transcribe what the review Ephemerides Liturgicae published in 1955, pp. 58-59.

Fr. Dominic Pechenino writes:

I do not remember the precise year. One morning the great Pontiff Leo XIII had celebrated Holy Mass and was assisting another, of thanksgiving, as usual. Suddenly, he was seen to straighten his head, then to fixate on something above the head of the celebrant. He stared, without batting an eye, but with a sense of terror and wonder, changing color and features. Something strange and great happened in him.

Finally, coming back to himself, giving a light but energetic touch of the hand, he arose. He was seen to start toward his private study. His consort followed him with care and anxiety. They said to him: Holy Father, do you not feel well? Do you have need of something? He responded: Nothing, nothing. After half an hour he called for the Secretary of the Congregation of Rites and, holding out a sheet of paper, enjoined that it be printed and reach all the Ordinaries of the world. What did it contain? The prayer that we recite at the end of the Mass together with the congregation, with the supplication to Mary and the fiery invocation to the Prince of the celestial militias, imploring God to cast Satan into hell.

The recitation of that prayer, kneeling, was also ordered in that writing. The foregoing, which was also published in the journal La settimana del clero, 30 March 1947, does not cite the sources from which the news was drawn. But it results that the way in which that prayer, which was sent to the Ordinaries in 1886, was ordered to be recited was unusual. In confirmation of what Fr. Pechanino wrote we have the authoritative testimony of Card. Nasalli Rocca who, in his Pastoral Letter for Lent, sent to Bologna in 1946, wrote:

Leo XIII himself wrote that prayer. The phrase (the demons) who roam throughout the world seeking the ruin of souls has an historical explanation, referred to us more times by his particular secretary, Msgr. Rinaldo Angeli. Leo XIII truly had the vision of the infernal spirits that were gathering on the eternal city (Rome); and the prayer that he wanted recited in the whole Church came from that experience. He recited this prayer with a trembling and powerful voice; we heard it many times in the Vatican basilica. Not only that, but he wrote with his own hand a special exorcism contained in the Rituale Romanum (1954 edition, tit. XII, c. III, p. 863 ff.). He recommended the bishops and priests recite these exorcisms frequently in their dioceses and parishes. He recited it very frequently throughout the day.

It is also interesting to take into account another fact, which enriches even more the value of this prayer which is recited after each Mass. Pius XI wanted that, in the recitation of these prayers, there would be placed a particular intention for Russia (cf. his allocution of 30 June 1930). In this allocution, after having remembered the prayers for Russia, which he had asked even all the faithful to say in the anniversary of the patriarch St. Joseph (19 March 1930), and after having remembered the religious persecution in Russia, he thus concludes:

And so that all may effortlessly and without inconvenience continue is this holy crusade, we establish that these prayers that our predecessor of happy memory, Leo XIII, commanded to be recited after the Mass by the priests and faithful, be given to this particular intention, i.e., for Russia. Thus, the Bishops and the secular and regular clergy must take care to inform their people and those present at the Holy Sacrifice, nor may they omit the frequent recollection of the aforesaid to their memory. (Civiltà Cattolica, 1930, vol. III).

Thus we see the tremendous presence of Satan is held present with much clarity by the Pontiffs; and the intention that Pius XI added touched the center of the false doctrine sown in our time and which is still poising the life not only of of people but of theologians themselves. If, then, the provisions of Pius XI are not observed, it is the fault of those to whom they were entrusted; certainly, they integrate well with the charismatic events that the Lord has given humanity through the apparitions of Fatima, although being independent of them; Fatima was still unknown to the world then.