The WebAPI version focus handle the server side, this product don't contains client side logic, we provide the Leaflet and Openlayers as client side in sample is just a guide.
And I don't think your original logic don't need to requery data when the data get changed, unless your code cache the data somewhere. Because the cache is only work for fixed data, any data get changed, we need remove old cache and generate the new version.
So please make sure whether you cached the data in your original mvc project, or you directly modify the data in client side, and post the change to server side but not get response, that's why it don't need to query again.
If your project cache the data in client side, you should want to implement that by the client library you choose. If that's modify data in client side and only post the change to server side, you can do the same thing in WebAPI edition.