Multiple DNS systems query

My network is set up as below:

Internet > DMZ > Amber Zone > Green Zone

Green zone has an AD forest/domain: greenzone.com
Amber zone has an AD forest/domain: amberzone.com

Both zones uses their own AD for DNS resolution.

Any devices in either zone that need 80/443 services are pointed at proxy.greenzone.com on port 8443 in their proxy settings. This is open on the firewall between Amber and Green zones.

Proxy.greenzone.com has a route to both internal web servers and the internet.

In the Green zone, we use https:/tech.com as an easy way to point our users for Tech Help. For example:

https://tech.com/Support - IT Support
https://tech.com/Password - Password resets
https://tech.com/FAQ - How to's

...you get the idea.

Now, the issue we have is that if a user is on a device in the Amber zone, if they type https://tech.com/*anything* they get sent to the real (i.e. externally facing) www.tech.com website.

I need to find a way for any user on a device in the Amber Zone to be sent to OUR internal tech.com sites rather than the external one.

Any ideas?