WordPress Update Plugin Hook/Action? Since 3.9

I don’t think an action has been added. You can look at version details for any version and see any new actions added.

The WordPress Way to run code on plugin update is what is described here:

The proper way to handle an upgrade path is to only run an upgrade procedure when you need to. Ideally, you would store a “version” in your plugin’s database option, and then a version in the code. If they do not match, you would fire your upgrade procedure, and then set the database option to equal the version in the code. This is how many plugins handle upgrades, and this is how core works as well.

and with code example here:

function myplugin_update_db_check() {
    global $jal_db_version;
    if (get_site_option( 'jal_db_version' ) != $jal_db_version) {
        jal_install();
    }
}
add_action( 'plugins_loaded', 'myplugin_update_db_check' );