Hi  ruben,
In order to set active tab with content, you need to set the nav-item i.e. the LI with active class and tab-pane with active in class.
I have modified nav-tabs HTML and JavaScript code in which i removed the active class and based on the ViewBag object set the nav-item and tab-pane class.
Refer below modified code sample.
Controller
public class HomeController : Controller
{
    public IActionResult Index()
    {
        dynamic mymodel = new ExpandoObject();
        ViewBag.Tab = 0;
        return View(mymodel);
    }
    [HttpPost]
    public async Task<IActionResult> Index(int tab)
    {
        dynamic mymodel = new ExpandoObject();
        // Set ViewBag object.
        switch (tab)
        {
            case 1:
                ViewBag.Tab = 1;
                break;
            case 2:
                ViewBag.Tab = 2;
                break;
            case 3:
                ViewBag.Tab = 3;
                break;
            case 4:
                ViewBag.Tab = 4;
                break;
            default:
                ViewBag.Tab = 0;
                break;
        }
        return View(mymodel);
    }
}
View
@model dynamic
@addTagHelper*, Microsoft.AspNetCore.Mvc.TagHelpers
@{
    Layout = null;
}
<!DOCTYPE html>
<html>
<head>
    <meta name="viewport" content="width=device-width" />
    <title>Index</title>
    <link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" />
    <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
    <script type="text/javascript" src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/js/bootstrap.min.js"></script>
</head>
<body class="container">
    <form method="post" asp-action="Index" asp-controller="Home">
        <input type="text" name="tab" />
        <input type="submit" value="Set" />
    </form>
    <hr />
    <ul class="nav nav-tabs my-3" id="myTab" role="tablist">
        <li class="nav-item" id="profile-tab1">
            <a class="nav-link" data-toggle="tab" href="#Well" role="tab" aria-controls="profile" aria-selected="false">Well</a>
        </li>
        <li class="nav-item" id="profile-tab2">
            <a class="nav-link" data-toggle="tab" href="#WellTest" role="tab" aria-controls="profile" aria-selected="false">Well Test</a>
        </li>
        <li class="nav-item" id="profile-tab3">
            <a class="nav-link" data-toggle="tab" href="#WellCore" role="tab" aria-controls="profile" aria-selected="false">Well Core</a>
        </li>
        <li class="nav-item" id="profile-tab4">
            <a class="nav-link" data-toggle="tab" href="#WellTop" role="tab" aria-controls="profile" aria-selected="false">Well Top</a>
        </li>
    </ul>
    <div class="tab-pane fade show" id="Well" role="tabpanel" aria-labelledby="General-tab">
        <div class="card-body">
            <div class="row">
                <div class="col">
                    <span>
                        This isi Tab 1
                    </span>
                </div>
            </div>
        </div>
    </div>
    <div class="tab-pane fade show" id="WellTest" role="tabpanel" aria-labelledby="General-tab">
        <div class="card-body">
            <div class="row">
                <div class="col">
                    <span>
                        This isi Tab 2
                    </span>
                </div>
            </div>
        </div>
    </div>
    <div class="tab-pane fade show" id="WellCore" role="tabpanel" aria-labelledby="General-tab">
        <div class="card-body">
            <div class="row">
                <div class="col">
                    <span>
                        This isi Tab 3
                    </span>
                </div>
            </div>
        </div>
    </div>
    <div class="tab-pane fade show" id="WellTop" role="tabpanel" aria-labelledby="General-tab">
        <div class="card-body">
            <div class="row">
                <div class="col">
                    <span>
                        This isi Tab 4
                    </span>
                </div>
            </div>
        </div>
    </div>
    <script type="text/javascript">
        window.addEventListener('load', function () {
            var tabVal = '@ViewBag.Tab';
            // Remove the nav-item active class.
            var navLinks = document.querySelectorAll('.nav-item');
            navLinks.forEach(function (link) {
                link.classList.remove('active');
            });
            // Remove the tab-pane active in class.
            var tabPane = document.querySelectorAll('.tab-pane');
            tabPane.forEach(function (pane) {
                pane.classList.remove('active');
                pane.classList.remove('in');
            });
            if (tabVal !== "") {
                // Set the class to activate the tab with content.
                if (tabVal == 0) {
                    document.querySelector('#profile-tab1').classList.add('active');
                    document.querySelector('#Well').classList.add('active');
                    document.querySelector('#Well').classList.add('in');
                }
                if (tabVal == 1) {
                    document.querySelector('#profile-tab1').classList.add('active');
                    document.querySelector('#Well').classList.add('active');
                    document.querySelector('#Well').classList.add('in');
                }
                if (tabVal == 2) {
                    document.querySelector('#profile-tab2').classList.add('active');
                    document.querySelector('#WellTest').classList.add('active');
                    document.querySelector('#WellTest').classList.add('in');
                }
                if (tabVal == 3) {
                    document.querySelector('#profile-tab3').classList.add('active');
                    document.querySelector('#WellCore').classList.add('active');
                    document.querySelector('#WellCore').classList.add('in');
                }
                if (tabVal == 4) {
                    document.querySelector('#profile-tab4').classList.add('active');
                    document.querySelector('#WellTop').classList.add('active');
                    document.querySelector('#WellTop').classList.add('in');
                }
            }
        });
    </script>
</body>
</html>
Screenshot
