I have a small project with two developers. I'm the owner of the project. I added an issue and assigned it to my partner. I got an email notification that a new issue was created and assigned to my partner (which is appropriate, as I'm the project owner). My partner, however, was never notified. I can find no configuration setting in the project or our accounts that discusses issue assignee notifications.
Assignees should obviously be notified when they have new issues to work on.
(For what it's worth, I am able to send my partner messages through BitBucket by visiting his profile, so I know his account's email address is configured properly.)