First of all, there is no concept of Postback in MVC. That is a Web Forms strategy of passing data to a server. Controller does not do any postback to view. What you have to understand is that controller is in charge of, lets say, preparing the information. This information is passed to a view to be presented in a way that View finds it fit. The controller returns a result and says which view should be used in order to satisfy user's request.
Users can submit data from the client using forms in a view to an action in some controller. Controller receives the information, processes it in a specific way and does something with it, like storing it in some data source. This is not a concept of postback like in Web forms.
What you described in your question is a way SPA application works, but you have to understand that even in SPA application the views are not always preloaded. This is true especially if you have a large application.
Downloading views, actually partial views, via Ajax is perfectly normal so it is not something that you should avoid at all cost. Later when you fetch a view via Ajax you can apply jQuery filters and special effects.
UPDATE: Controllers return action results. The base class for these results is, as you my have guessed ActionResult. Many other classes inherit from this class. For example, ViewResult is the most often used and is the subject of this answer. You also have FileResult that you use to return files, RedirectToRouteResult to perform redirection, and so on. All these are action result. Returning a view in MVC means: "In order to display this data to a user, please use this view or partial view."
When you request (issue HTTP GET method), a controller will return a view to you, and when you post data (issue HTTP POST method) a controller will do something and can perform redirection after which it normally returns a view, or return a file, etc. Postback in MVC in essence does not exist. For example, in Web Forms if you click on a button or change a value in a drop down box that has AutoPostBack set to true, the post back is initiated and the ViewState is sent to the server. MVC does not have that sort of mechanism to trigger postback. You either submit a form or use Ajax to perform GET request to retrieve information or POST to submit data as JSON back to the server.
So, when you make a request to see the page it is not a postback. When you post form data to the server it is not a postback, it is submitting the data and is not the same as Web Forms postback.
I hope this helps you now.