A great deal of what is now printed alongside the seventy-two angels entered the tradition in the 1880s and 1890s.
The Hermetic Order of the Golden Dawn built a comprehensive system of correspondences, in which every element of every subsystem it used was cross-referenced against every other: sephiroth, Hebrew letters, planets, zodiacal signs, decans, tarot cards, elements, colours, plants, stones. Aleister Crowley published the tabulation as Liber 777 in 1909, and Israel Regardie published the order's papers as The Golden Dawn from 1937, which is how the material reached the general public.
The relevant part here is the tarot attribution. The Golden Dawn assigned the thirty-six minor arcana from two to ten in each suit to the thirty-six decans, in a fixed sequence beginning at the first decan of Aries. Every Shem angel, holding half a decan, therefore inherits a card. That is where the card printed beside each of the seventy-two comes from.
The choir and sephirothic assignments, Seraphim under Metatron for Kether, Cherubim under Raziel for Chokmah, and so on down, in nine groups of eight, are older than the Golden Dawn but belong to the same enterprise of total correspondence. The nine choirs are from Pseudo-Dionysius, whose Celestial Hierarchy is a Greek Christian text of around the year 500. The sephiroth are Kabbalistic. The mapping of one onto the other, eight angels to each of nine rungs, is Christian Kabbalah doing what it did everywhere.
None of these layers is illegitimate. The problem is that they are usually presented without dates, so that a fifth-century Christian hierarchy, a medieval Jewish counting technique and a Victorian tarot scheme appear in one sentence with equal authority.