The mechanics are simple. Degrees are counted from one, not from zero, so anything from 0 degrees 0 minutes to 0 degrees 59 minutes of a sign takes that sign's first symbol, and a planet at 8 degrees 30 minutes of Virgo takes the ninth of Virgo. In practice astrologers look up the symbol for a small number of chart points rather than all of them: the Sun, the Moon, the Ascendant, the ruler of the chart, and the degrees that eclipses and new moons fall on. The other common use is in prediction by solar arc or secondary progression, where a slowly moving point crosses one degree at a time and each symbol is read as the theme of a period.
There is a real disagreement about the rounding. A minority school reads the symbol for the degree a planet has completed rather than the one it occupies, which shifts every reading by one image, and there is no way to settle it from within the tradition.
The sceptical reading is not difficult to state. The images are transparently of one place and one decade: automobiles, telephones, ocean liners, flags, prospectors, and a recurring cast of Native American figures drawn from 1920s popular stereotype rather than from any particular nation. A source outside a single mind would not date so precisely to San Diego in 1925. The procedure had no controls of any kind, Jones prepared the cards, administered the session, recorded the answers, and published the account, and there is no second witness to any part of it. And the set is one of at least three complete 360-image series produced within thirty years of each other, which suggests that the achievement lies in the sustained effort of imagining 360 scenes rather than in reception from elsewhere.
None of that settles what the symbols are worth in use. A working astrologer's defence is that a degree symbol is a prompt for interpretation rather than a claim about the world, and that an image which is arbitrary in origin can still do useful work as a focus for attention. That defence is coherent. It also concedes the historical question entirely.