However some servers will rewrite the mail serverside to match the authentication user to prevent spam. The main service I know that does this is gmail (and probably any of the “big” mail providers). If you send through a more basic typical Linux server it will send as the “correct” address.
Although these days it’s mostly a bad idea to do that because you’ll hit issues with SPF, DKIM, etc.
The main actual issue you have here is if you manually hit “new message” then you need to think about which sender to choose if you’re coming from a unified inbox view instead of the specific inbox for the account you want to send from.
Unless you flip the setting to always send it from one address.