When you query the Domain Name System (DNS) to find the domain name(s) associated with an IP address, that is called a Reverse DNS lookup or reverse DNS resolution (rDNS). It is called a «reverse» lookup because it is the reverse of the usual DNS lookup, which is used to find the IP address associated with a domain name.
DNS lookup: domain = IP
rDNS lookup: IP = domain
Having reverse DNS entries in place is best practice, but it has become especially important for services like email since many mail servers will not accept messages from IP addresses without reverse DNS entries.
DNS changes take a bit of time to propagate throughout the internet, and that period varies depending on a number of factors. Typically though, after tech support adds reverse DNS, the changes shouldn’t take more than a few hours to propagate.