If you would like to keep track of what is going on with your WordPress CMS inside out, no matter who login your site or a plugin is being updated. You can keep track of it by using Activity Log plugin.
You can define what should be log and what shouldn’t. This plugin has over 90,000 downloads with 4+ star rating.
After download and activation, you can select wide range of activity to be log. E.g. I’ve setup notification about plugin update and you can define how many days you would like to keep the log.
Once the pre-set condition is met, the email notification will be sent immediately so the pre-set email receiver will know what is going on with the WordPress site.