When you point your domain name to our nameservers or anywhere else for that matter, this process will trigger the so-called DNS propagation which can last for up to 72 hours before your domain starts resolving to the new host. DNS propagation is the time the internet service providers across the globe need to clear their DNS cache so they can update your domain's new DNS information. During this period, you may experience connection problems towards your domain, or you may still see the site on your old hosting provider.
Note that each ISP is different and the time it takes them to clear their cache can vary, which means that some people will be able to access the site on the new environment before you. In such situations, all you need to do is be patient, as when the DNS caches are updated world-wide you will once again be able to access the site on your end. What you can do in order to ensure that the problem is not isolated on your end is to clear both your computer's DNS cache and your browser's cache.