People in any role should see the most recent textual content.
You and your team need to consider these steps, and do them at an agreed-upon regularity.
As books are added or updated in Paratext, someone must use Send/Receive in Paratext to keep the Paratext repository up-to-date.
In Scripture Forge, when someone initially connects a project the latest content from the repository is received.
Then, as books are updated in Scripture Forge, the person with the role of project Administrator must synchronize the Scripture Forge project with the Paratext repository.