This is definitely weird. A few things could be happening
Are all the emails for the same WordPress install?
If yes:
1) Are they all going to the same email address?
I have been working as a Contract WordPress Developer for ten years and the one time we had this issue we were pulling our hair trying to figure out why they were getting the notification so many times when they only had one site and we finally realized that the email accounts for all of their admin user accounts were receiving the email and they did not check all those accounts daily. This particular client I am referring to had 5 admin accounts because they kept using internal generic addresses when hiring contractors.
2) If it is one install would be that they are not getting the default email that says the site has been updated. a Default email should look something like this, just with more recent version numbers:
Howdy! Your site at http://www.YourSite.com has been updated automatically to WordPress 4.1.4.
For more on version 4.1.4, see the About WordPress screen:
http://www.YourSite.com/wp-admin/about.php
WordPress 4.2.1 is also now available. Updating is easy and only takes a few moments:
http://www.YourSite.com/wp-admin/update-core.php
If you experience any issues or need support, the volunteers in the WordPress.org support forums may be able to help.
https://wordpress.org/support/
Keeping your site updated is important for security. It also makes the internet a safer place for you and your readers.
The WordPress Team
3) If my suggestions in #1 and #2 are not the root of the problem then maybe previous developers the client was working with created development sites that are still out there being updated. Make sure the URLs in each and every email are their domain name.
If none of those situations are the root of the problem then the other then unfortunately, the only other thing I can think of is that would be that there is some malicious code running somewhere on the site causing the emails to be sent out and you need to look into testing the site for malware.
Sorry I was so long winded there but I certainly hope that helps!
