When you perform a redcirect in an AJAX response, you're essentially redirecting the response itself, not which page the request is being made from.
I like to think of this as having 2 separate cars on 2 separate roads traveling parallel to each other. When you make an ajax request from the first car, you're essentially yelling over at the other car on that other road to tell them to do something. If you tell that car to turn left it will turn left, but the first car doesn't change direction, it just keeps moving forward.
In order for your application to actually perform a redirect in that first car that's still going straight you need to get some kind of response from the second car that may say something like "I can turn left, but it won't do you any good. Why don't you turn left instead?".
In code, this can be represented by rather than performing your redirect in your rails controller, instead perform the redirect in your AJAX response.
Something like this might be more appropriate...
.success($.proxy(function(data, xhr) {
window.location.replace("/home");
},this));
See also another Stack Overflow article on redirecting after an AJAX response.
How to manage a redirect request after a jQuery Ajax call