You can do the program as long as you are enrolled in any college! The only thing is, you can't be a first semester freshman when you apply. You can apply once you finish your first semester.
But, only a select few colleges will give you credits for the program. Talk to your advisor and he/she can tell you more about it.
That's incorrect "first semester freshman may apply to participate in their second semester" as per the dcp website. You just cannot apply to use DCP as your first semester. As long as the student completed their first semester prior to their arrival date. Advisors may advise against applying during the first semester but Disney's requirement is listed below. Source: Disneycollegeprogram.com