I fixed this issue and got the Submit method to be called when Upshot invokes _commitChanges.

I changed the default api route from: 

routes.MapHttpRoute(
name: "DefaultApi",
routeTemplate: "api/{controller}/{id}",
defaults: new { id = RouteParameter.Optional }
);

to:

routes.MapHttpRoute(
name: "DefaultApi",
routeTemplate: "api/{controller}/{action}",
defaults: new { action = RouteParameter.Optional }
);