The sign your DC is in indicates, in a very general way, the traits of people you attract and are attracted to. For a woman (or man) with the DC in Aries, whoever they prefer as a partner, and whoever they draw into their life, has some significant Aries-like traits, or brings out the Aries in the native, or both.
If you have your DC in Aries, perhaps you have a competitive streak and you draw in partners who are fellow competitors. Perhaps you draw in people who like adventure and challenge, and you enjoy doing those things together. Perhaps you draw in people with quick tempers, or who've experienced much challenge in their lives. Perhaps your partner is a soldier, an entrepreneur, a professional athlete, or something else along those lines--all those professions are Aries-like.
More often than not, a person with strong Aries-like traits has a significant placement in Aries, but not necessarily their sun. It could just as easily be their moon sign, rising sign, or a sign where they have planets concentrated. It's also possible that Aries is an empty sign for them but they have other chart placements that indicate those traits.
So it's way too simplistic to say that if you have your DC in Aries, you attract/are attracted to Arieses. Aries people, yes, but not necessarily people born in the last week and a half of March or first three weeks of April.