Hey @Jack Etherington 👋 Jacques here from Support Engineering.
With balanced assignment, conversations should wait in the team inbox until a member of that team who is active and has not reached their assignment limit is available to take on more conversations. If you are active in Intercom during EMEA office hours and not during APAC/AMER office hours, normally, you should only be assigned conversations from the EMEA inbox. Conversations in the APAC/AMER inboxes should remain there until their respective office hours begin, assuming that the Balanced Assignment is set up correctly with the right team memberships and office hours.
However, if you are being assigned conversations from APAC and AMER outside of their office hours, it could indicate that there might be a misconfiguration in the Assignment settings or team memberships.
I would review the Balanced Assignment settings and ensure that your team memberships are correctly defined so that you are only a member of the EMEA team during its office hours. Additionally, check that your status is set to active only during EMEA office hours and that your assignment limit is properly configured.
Hope this helps!