How does office365 automatically authorize users in a domain?

Question

User identification

Good afternoon!
There is a Domain on Windows Server 2012 R2 (intra.domain.com), and an Office 365 Business subscription (accounts - @domain.com). There is no synchronization between the domain and office365 and communication is managed separately.
In the profile of each user in the domain, his email is entered - [email protected]
I create a user in the office, he enters portal.office.com with the login [email protected] , installs the office using the link and is automatically logged into the office with a domain account - [email protected] and the office considers itself successfully activated.
Can experts explain how it works and is it possible to leave it like that or is it better to log in under the office365 account - [email protected]?
The terminal server has a standalone office 2013 pro plus with an Open License (not related to office 365 in any way). I don't know if there is any connection.
Thanks for the possible ideas.