Although people in urban areas often adopt things (fashions, technology, etc.) before those in more rural areas do, there is another factor that causes culture to change. Hollywood is often what drives change, as does the fashion industry. So it seems that industries--which do exist in the urban environment--are the ones always effecting change; the rest of us choose whether or not to adopt the various new modern technologies, fashions, and beliefs they feed us.
Culture is a way of living for a group of social beings. Urbanism only deals with how people are living in the inner city and does not include the suburbs. Some cultural fashion and music could get to the suburbs but most likely urbanism will remain in the inner cities.