This article is relevant to you if your organization has fully transitioned to Exchange Online and decommissioned your last on-premises Exchange server. 
Here are the most frequently asked questions and encountered issues.
How does Adaxes work with Exchange Management Tools (EMT)?
Adaxes does not use the Exchange Management Tools, and there is no setting to force it to do so.
Adaxes does not require EMT to manage mailboxes. Instead, Adaxes performs all necessary Exchange operations directly in the cloud using the Exchange Online PowerShell V3 module, provided your Microsoft 365 tenant is registered in Adaxes.
Why am I seeing errors when performing Exchange operations?
If you did not fully uninstall the last Exchange server but powered it off instead, Adaxes will treat your environment as having on-premises Exchange. This happens because the information about the last Exchange server is not removed from AD if it is not uninstalled. 
You may see harmless error messages when performing certain Exchange operations on users with remote mailboxes. Adaxes performs the operation in Exchange Online, but also attempts to connect and run cmdlets against the missing on-premises server. The operation succeeds but you still see an error.
Also, actions exclusive to on-premises Exchange, such as Create mailbox and Mail-enable, will remain visible in Adaxes, even though they cannot be successfully executed. Attempts to execute them will always fail.
What should I configure in Adaxes?
To prevent unnecessary connection attempts to the missing server, specify your forest as one where Exchange is not managed by Adaxes. You will retain the ability to manage Exchange Online mailboxes as normal.
Leave remote mailbox settings, as is. Adaxes will not attempt to create remote mailboxes because you no longer need them. To provision mailboxes for new users, simply assign Exchange Online licenses to these users.