And see if Mail is selected as a start up item.

1. Right-click the Mail icon in dock. See OPTIONS. Make sure "Open at Login" is not checked.

2. If already unchecked, do this:

2a. Quit all apps, Mail first.
2b. Shutdown. Wait 1 full minute. Reboot.
2c. If mail still opens, you probably have what is called a "daemon" (basically a hidden program). At this point, if you still have an automatic login, it may be time to consult a professional.

Perhaps you're seeing what I used to see. I would normally leave the Mail app running, but with all of its windows closed. And maybe once a day it would open a "viewer" window -- for no apparent reason.

Changing my habits to quit Mail (and not just close the window) was a tolerable workaround.

But I believe upgrading to the latest OS has fixed it ... I've not seen this behavior in several months now.

Hope this helps!