For starters, it's not recommended to have more than one RODC per site (to ensure consistent caching behavior). Regarding the behavior you're seeing, verify the following:
- There is a separate site representing the DMZ location
- The DNS records reflect the fact that the site coverage is provided by RODC
- You have cached the passwords of the computer accounts in DMZ, in addition to user accounts
If the above response helps answer your question, remember to "Accept Answer" so that others in the community facing similar issues can easily find the solution. Your contribution is highly appreciated.
hth
Marcin