Hi john marker, thanks for the question.
There are a few ways you can do this workflow. One way is with online services, or "Feature Services" as that sample demonstrates. In that workflow any features you add to the service and push up to the service will be available on the service, but you can control who has access a few different ways. One way is with Ownership Based Access Control:
OwnershipBasedAccessControlInfo QML Type | ArcGIS for Developers
Documentation for ArcGIS Enterprise
But if you are more concerned about keeping this information private, it can be stored in a feature service that is password protected. The ServiceFeatureTable class can access secured service that require credentials.
An important distinction to be aware of is that a FeatureLayer will visualize any FeatureTable data, and there are a few options. The method showcased in that sample is using a ServiceFeatureTable; an online service.
A FeatureLayer can also visualize data from a Geodatabase via a GeodatabaseFeatureTable, in which case all data would be stored offline and never pushed to any online service.
>So my features that I add to a map will be pushed onto the server? Say these locations are supposed to be private. What are the measures taken to on the server side, so they can't be accessed?
A secured feature service would be an option, see above.
>Is there a way to save the points locally?
Yes, with using a GeodatabaseFeatureTable.
FeatureLayer QML Type | ArcGIS for Developers
GeodatabaseFeatureTable QML Type | ArcGIS for Developers
Here is a sample that shows how to visualize data from an offline Geodatabase.
Feature layer (geodatabase) | ArcGIS for Developers
