When you change the nameservers of a domain, it takes some time to update the nameservers. This period is called DNS Propagation. During propagation, you may notice some abnormal activity of your domain/website like, one person may see the new server while someone else sees the old one, yourdomain.com may work while www.yourdomain.com may not work etc. These abnormal activities are actually normal during the DNS Propagation.
Normally DNS Propagation may take upto 24-72 hours. So if you getting these types of issues within this time, there is nothing to worry actually. But everything must be fine within this period. If you are facing any issue after 72 hours, then there is something wrong. You should contact your hosting service provider.
In short, DNS propagation depends upon how frequently the DNS master cache nameservers of your ISP are refreshed.