Once you have setup the Free Email Service for your domain name, you need to modify your Name Servers to the ones specified by Hostgator India. Generally, the Free Email Service should start working within a span of 24-48 hours post modification of Name Servers.
Do not be confused when you an encounter an error while using some DNS Tools like DNSReport.com:
No NS A records at nameservers
This does not indicate an error and will not affect the Email Service of your domain name.