My family pretty much believes that a girl becomes a woman only when she gets married, and that single women must stay in their father's home, but they also believe in arranged marriages. :/
I wouldn't go to that extreme, but to me the average undergrad age person is not an adult. There are, of course, exceptions, based often on how well their parents prepared them to be an adult.
While US society often has a cut-and-dry age of 18 as the age where one gains adult responsibility, I believe our culture would be much better off if the voting age was back to its original age of 21, and if teenagers were given the responsibilities they had even two generations ago.
In short, while I see adulthood as something that you grow into, I believe that parents should lessen the rules and restrictions they would have when the child was a teenager on grown children at home, so the person can grow in trustworthiness, but that they aren't really adults unless they have moved out of the home, unless they're paying the going rate for rent on their bedroom and their portion of the food, and are otherwise self sufficient.
I understand that from time to time even if money had been carefully used, that there might not be enough to cover needs, and I believe that parents should, in that case, help out if absolutely needed (and if they had seen that they didn't waste money on a Nintendo Wii or whatever if they had to buy groceries), but in general should let the young person live with their own choices if their money was not well managed.