I cannot say what the Ven. Buddhaghosa Thera's authority is for his statements in the Atthasālinī and elsewhere about the A.P. It was certainly the generally believed tradition at that time that the Buddha himself had taught it to the devatās; and I seem to remember that the Chinese pilgrims to India (I forget their dates) were shown the place where the foot of the triple staircase rested down which the Buddha was said to have descended after the Vas season in question.
But though the tradition is certainly earlier than the Ven. Buddhaghosa Thera's time, there is a further complicating element. Each of the early Hīnayāna schools (let alone the Mahāyāna) seems to have had its own particular Abhidhamma Pitaka, though the Suttas and (for the most part) the Vinaya were held in common (I speak from memory of past readings). In consequence, the question might have arisen (though I don't know that it actually did), which of the various A.P.s the Buddha taught to the devatās. There may be earlier books than the present Commentaries reporting the tradition, but I do not know of them. And I do not recall whether the Ven. Buddhaghosa Thera quotes his authority, but I think not. (If you are interested, the Atthasālinī is in English translation as The Expositor.)
The Suttas themselves record the earlier part of the Buddha's ministry in some detail, and also the last few months; but there is no connected narrative of his movements and actions in between. But in any case I am not aware that any Sutta says that the Buddha taught the Abhidhamma Pitaka, or even abhidhamma, to the devatās, or that he spent a Vas season in Tāvatimsa. Upon occasion the Buddha did visit various heavens (e.g. Brahmanimantanika Sutta, M. 49: i,326) but for the most part, so it seems, the devatās came and listened to the Buddha teaching human beings (and attended in great numbers), e.g. Cūlarāhulovāda Sutta, M. 147: iii,278-80; Pātika Suttanta, D. 24: iii, 31-35. There seems to be no reason to suppose that the devatās are superior to human beings in intelligence (in whatever other way they may be superior). The actual teaching given by the Buddha to Sakka, chief of the Tāvatimsa deities, is recorded in the Sakkapañha Suttanta, D. 21: ii,263-80; also Cūlatanhāsankhaya Sutta, M. 37: i,251-56.
[82.1] Chinese pilgrims: Fa Hien (Fa Hsien) travelled from 399 to 413 A.D. Translations of his report are available as A Record of Buddhist Kingdoms (London: Oxford University Press, 1886, tr. James Legge) and as A Record of the Buddhist Countries (Peking: The Chinese Buddhist Association, 1957, tr. unidentified). The account by Hiuen Tsiang (Yuan Chwang) of his travels has been translated by Samuel Beal in Buddhist Records of the Western World(London: Kegan Paul, Trench, Trübner & Co., n.d.). Hiuen, who was in India between 629 and 645 A.D., was primarily concerned with differences in points of Vinaya practice: he returned to China with hundred of texts. [Back to text]