Hi HSAB,
To troubleshoot the issue, I would like to confirm if you have deployed an Exchange Hybrid. Generally, Dirsync will one-way sync from on premise objects to Office 365. If you want on premise to show entire GAL(domain1, domain2, etc), you can refer to the following brief steps to achieve the goal:
1. Create normal local AD users in the local AD. You can use ADUC to do it.
2. Use SMTP match to match these local AD users with the existing online mailboxes.
3. Enable remote mailboxes for the local AD users after SMTP match.
As a tip, you need to add domain2, domain3, and domain4 as domain suffixes in AD. I suggest creating a test user to connect to a test online mailbox using the steps above before deploying the steps for the currently existing online mailboxes.
Moreover, I would like to explain some cross premiss features are not available in Hybrid. For example, on premise users will not view the shared calendars from cloud users and vice versa. This is not a Microsoft supported scenario.
Thanks,
Johnny Zhang