There's no specific age that marks when you should stop going to las posadas. It's really more of a cultural and family thing. What you see in your family is pretty normal: there are people who participate from childhood all the way to their 80s, and others who stop going at 15. It all depends on how important the tradition is to each family and what meaning they give it.
The most common thing I've seen across different regions is that people keep going as long as they're having fun and feel like they're part of the tradition. Your cousins who are 20 and 25 aren't out of place at all; many families value having young adults keep the custom alive. What your aunts call "grown-up stuff" is really more of a shift in personal priorities than something that's required based on age. If your cousins enjoy las posadas, they should keep going. The tradition is meant to be experienced as a family, no matter how old you are.