Replies use the correct account, even though the From field shows the wrong account.
Users with POP3 or IMAP accounts who created Outlook.com accounts using their own email address, to sync just their calendar and contacts have noticed a problem (bug!) after their account was migrated to the new server and opened in Outlook 2016: all replies use the Outlook.com account, not the account that downloaded the message.
New messages use the correct email account but replies or forwards always show as From the Outlook.com account. At this time, the correct From account is actually used, even though it displays the wrong account. Test it, and if it sends from the wrong account, select the correct account using the From selector. Yes, it's an extra step that should not be necessary.
My best guess on the cause of this bug is that it is related to a new Outlook 2016 feature for Outlook.com accounts that lists all aliases for your Outlook.com account on the From selector, allowing you to use any of select any of the aliases to send from. (Exchange users have wanted the ability to send using the secondary addresses assigned to their mailboxes for years but it's only available in Outlook.com accounts at this time. Sorry.)
Note: those addresses are only used for testing. I will not respond to messages sent to those addresses (and probably won't even see them.)
In my tests, Outlook.com accounts with non-Microsoft addresses added as aliases and the new custom domains are affected. If you only have Outlook.com aliases (including Hotmail, Live, MSN), Outlook will use the correct From account.
Affected users have limited options until this is fixed. You can continue to change the From address manually or remove the non-Microsoft address from the Microsoft account. Macros to change the address automatically are not working.
Removing the address is not going to work for custom domains, but will work for anyone who is using a Pop3 or IMAP account and Outlook.com for calendar and contacts. The address can be added back as a connected account then set as the default for sending, which might work better.
To remove an address alias from your Microsoft Account, log into your account at https://account.live.com/names/Manage then click Remove next to the addresses you want to remove.
The following addin works around this bug (also works if you just always want to send from one account.)
If you have more than one email account collecting email and always want to send replies using the default account, Outlook always uses the receiving account when you reply. You can select the correct sending account when you reply, but it's easy to forget to do this. This utility also fixes the Outlook.com bug where the Outlook.com account is used for all replies.