I have Exchange 2016 on-premise multi region. Email flow goes from internal to Edge to third party cloud to internet. Hybrid is installed using classic mode and centralised email flow was selected.
I have outbound connector in O365 pointed to cloud provider with address *. I have second connector pointed to Edge servers with route all accepted domains selected.
O365 to on-premise keeps going via the 'O365 to cloud' connector despite the second connector being more applicable. I i disable the 'O365 to cloud' connector the second connector kicks in. The 'O365 to cloud' was created by the hybrid wizard and i notice in order to allow the '*' address space to function the connector has the 'RouteAllMessagesViaOnPremise' value set to true.
The on-premise domains in O365 are configured as InternalRelay following advice from MS support.
We've spoken to MS and they tell me the connectors should work perfectly however this is not the case.
What i'm trying to make happen is all email flow for my internal domains flows by my Edge servers and all other emails flow via my O365 to Cloud provider and then onto the internet.
you can try CBR to force emails to use a connector, for example for O365 to your cloud email security provider, you can create a transport rule to route all emails to the connector if sender is inside the org and recipient is outside the org , this should force all external emails to go through the connector you want it to.