MVC4 No update on selchange DropDownList Postback - asp.net-mvc-4

Question

After I have changed selected item in my DropDownList everything works fine. But the view doesnt show the newly selected item (value) in the view.
In my code there is #Model.Name What is wrong? I have already spent do many hours on this problem!
My controller looks like this:
//
// GET: /Province/
public ActionResult Test()
{
ModelState.Clear();
var items = _ProvinceService.GetAll();
ViewBag.Lista = new SelectList(items, "Id", "Name", -1);
var province = _LandskapService.FindByName("xyz");
return View("Test", province);
}
// POST /Province/Test
[HttpPost]
public ActionResult Test(int provinceId)
{
if (ModelState.IsValid)
{
ModelState.Clear();
var model = _ProvinceService.GetAll();
var province = _ProvinceService.FindById(provinceId);
ViewBag.Lista = new SelectList(model, "Id", "Name", province.Id);
return View("Test", province);
}
else
{
return View();
}
}
And here is the view:
#Html.DropDownList("dropDownList3", (SelectList)ViewBag.Lista, "-- select province", new { onchange = "UpdateProvince()" })
<table style="border-collapse:collapse">
<tr>
<th style="width:200px">Name</th>
</tr>
<tr>
<td> #Model.Name </td> Here is the problem: #Model.Name is correct but the view dont show it. Old value is displayed. But debugger shows right value (the selected value).
</tr>
function UpdateProvince() {
alert($('#dropDownList3').val());
var SelCat = $("#dropDownList3").val();
var text = $("#dropDownList3 option:selected").text();
var value = $("#dropDownList3 option:selected").val();
if (SelCat != 0) {
var url = '#Url.Action("Test", "Province")';
// $.get(url, {provinceId : value});
$.post(url, { provinceId: value });
}
}