While people are aware of western horoscopes, their actual connection to a Gifted's powers hasn't really come to light. Because a person's sun power often doesn't correlate with their sun sign, most people don't have any reason to suspect that the powers they wield are directly tied to the stars themselves. There are definitely some fanatics out there who have theorized that the positions of planets in a person's full horoscope might indicate how their power further develops, but actually awakened Gifted have only begun to increase in frequency recently. The last big boom of Gifted resulted in the war between the government and the past organizations, but before that they were very rare among the population. So, yes, while there are a handful of people out there who believe their powers are tied directly to their signs, they're a very distinct minority - and most people don't give their theories any credence.

But yes, people's powers are affected by their signs, it's just that there's such a small sample size (especially of people who awaken their moon, ascendant, etc.), that there isn't enough data available in-game for them to confirm it as such.