RedirectToAction in JavaScript does not work

After a validation I call the controller in the action (Add) to add a new record through javascript.

If the insertion succeeds I give RedirectToAction to the index of this same controller passing the id of the profile that I just registered, however nothing happens!

JavaScript:

function validaFormulario() {
    var formularioValidado = false;

    formularioValidado = validaFormulario();

    if (formularioValidado) {
        var perfil = obtemPerfilDoFormulario();
        $.ajax({
            type: 'POST',
            url: '/Perfil/Adiciona',
            data: {
                "perfil": perfil
            },
            async: false,
            error: function (xhr, status, error) {
                alert(error);
            }
        });
    }
}

Controller:

public ActionResult Adiciona(Perfil perfil)
{
    PerfilDAO perfilDAO = new PerfilDAO();
    perfil.UsuarioId = usuario.Id;
    perfilDAO.Adiciona(perfil);

    EnviaEmailRecebimentoCadastro(perfil.Email);

    EnviaEmailAtivacaoDeConta(perfil.Email);

    return RedirectToAction("Index", "Perfil", perfil.Id);
}

I was able to get around the problem by sending the profile id by Json and manually doing the redirect by adding the javascript "success" return.

Would this approach be correct? I am starting in web development and wanted guidance on these "good practices". After all,% w / w of my controller should work. Where did I make the mistake?

Code with problem bypassed:

Controller sending Json:

public ActionResult Adiciona(Perfil perfil)
{
    //restante do codigo

    return Json(perfil.Id);
}

Javascript with success:

    $.ajax({
        type: 'POST',
        url: '/Perfil/Adiciona',
        data: {
            "perfil": perfil
        },
        async: false,
        success: function (data) {
            var id = JSON.parse(data);
                window.location.href = "/Usuario/Lista/" + id;
        },
        error: function (xhr, status, error) {
            alert(error);
        }