Hi
IP Customization is only going to happen during a planned recovery or disaster recovery, not during the test of a recovery plan.
During the test your protected VMs will not be powered off so you do not want to have your VMs running in two places even if they are using different IPs because there might causes other issues, so only during the test the VMs will be powered on in an isolated network
During a planned or disaster recovery your VMs will use the port group you picked during the protection of the VM and the ip customization will happen, and about your DNS if you do not have dynamic updates enabled you would need to manually update your records.
Best regards