The parameter names in your action and route must match. You can either change your action to:
[HttpGet]
public List<TagModel> Tags(int id)
Or change your route to:
config.Routes.MapHttpRoute(
name: "RouteForHandlingTags",
routeTemplate: "api/v1/{controller}/{contactId}/{action}",
defaults: new { },
constraints: new { id = @"\d+" }
);
Note: you do not need [FromUri] with a primitive type like an int.