Domain Mapping Using IP in lieu of Domain Name

We are moving the client to a new host.
Prior to moving we are adding new sites.
The URL will stay the same and is still pointed at the live sites.
When I try to substitute the IP address of the new server account for the domain name in Domain mapping, we get a site not found error message.
For example, http://residenceriverbend. yields the error whereas is a live site.
I have set up the host account with a wildcard sub-domain.
I suspect that since the DNS pointers are not pointing to the server, things may not resolve properly.
What would be the correct method for adding new sub-domain sites while in this development posture?

Thank you.