A domain and hosting are two separate products. The domain must be told which server holds the website.
FIND YOUR NAMESERVERS
Client Area > Services > My Services > click your hosting package. The nameservers for your account are listed there and in your welcome email. They will be either ns3 and ns4.zillionkinghost.com or ns10 and ns11.zillionkinghost.com.
Do not assume. The pair differs depending on which server your account was provisioned on, and using the wrong one leaves the domain unresolved.
IF THE DOMAIN IS REGISTERED WITH US
Client Area > Domains > My Domains > click the domain > Nameservers > Use custom nameservers > enter the pair > Change Nameservers.
IF IT IS REGISTERED ELSEWHERE
Log in at that registrar and replace the existing nameservers. The setting is usually called Nameservers, DNS Settings or Manage DNS. Remove any existing entries; do not add ours alongside another host's.
AFTERWARDS
Allow up to 24 hours, though a few hours is typical. Then run AutoSSL in cPanel.
If the domain still shows the old site after a day, open a ticket with the domain name and we will check the delegation.