Best approach to add new domain to O365

What is the approach to this in a best way? We are in the middle of a slow migration.
We need all users O365 @newcontoso.com to join the current O365 tenant @oldnewcontoso.com (example).

We have established a domain forest trust with O365 @newcontoso.com.
All AD accounts from O365 @newcontoso.com have been migrated to current Domain @oldnewcontoso.com. With that in mind, users are currently using two sets of credentials.
Users/computers from O365 @newcontoso.com are accessing OWA for @oldnewcontoso.com.
O365 @newcontoso.com has local on-premise Exchange server. We are not migrating email messages to O365 @oldnewcontoso.com on premise AD is already synching to AD connect/O365. We do not have local exchange.

I am thinking we need sync the AD accounts from O365 @newcontoso.com to AD connect and O365. Now there will be two AD accounts synching the same proxy email addresses causing conflicts, I think.

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