I figured it out, when registering with register_setting the second parameter is the name of the settings you will be saving and updating, the parameter is pass in here to whitelist it against being updated outside of the plugin. The AJAX callback is deemed outside of the plugin.
My register settings is below and the second option is the same as the one in get_option in my question. For the settings that I will be changing I will simply use a different name.
register_setting(
'user_manager_group',
'user_manager_options',
array($this, 'sanitize')
);