Problem with child theme

I am using the CyberChimps Responsive Child Theme v1.0.0 and I just have a question if I may. This is a website pedrosdigitalsolutions.com that I am just using to experiment on by changing css and looking into the file structures to see where everything is and how various styles etcetera change the appearance of a webpage. I have been inspecting the homepage with Firebug and have noticed that sometimes when I change some css by putting the relevant attributes into the style.css of the child-theme, the changes do not “take” and yes I have updated the file before I go back to look at the live homepage. Then I cut the modified code from the child-theme css and put it in the Dashboard>Appearance>Theme Options>CSS Styles section the change is then reflected on the live homepage.
I believe, from my limited knowledge base, that in some instances the main responsive theme (parent) style.css file will take precedence over any css modification placed into the child css file. But by the same token I would assume that both the areas that I am placing the modified css into are in the child section. What am I missing here and I do hope that my explanation makes some sense. What is it they say, a little knowledge is a dangerous thing 🙂 Thanks Pedro.