You can update your Share Point Add-in by using the updating support built into Share Point.
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Then upload the latest version of the add-in to your test site's add-in catalog and update every instance of the add-in.
Verify that each has the latest add-in version number and the latest version of all components.
But nothing in the Share Point infrastructure forces users to update.
So changes that you make to remote components must not break the older versions of the add-in.
A general, but not quite universal, rule is that you should things to remote components, but avoid deleting, renaming, moving, or changing the schema, connection string, or URL of any existing component.
If a remote component needs to know the version of the add-in instance that is calling it, you can pass this information from Share Point.
In particular, because the preview program for autohosted add-ins has been closed, you should be aware that you cannot update an autohosted add-in to a provider-hosted add-in.
You have to convert the add-in as explained in Convert an autohosted Share Point Add-in to a provider-hosted add-in.
Add and change components of the add-in as needed, and then test and debug them against the test site as if it is a brand new add-in you are creating from scratch.