LoggedInTemplate displayed in login page occasionally but I don't want it

I have a Site.Master page with LoggedInTemplate. Basically it works well. It appears after login and disappears after logout. However, if I have logged in in Tab A, and then enter the login page in Tab B, it turns out to be a login page with content that is supposed to display only after login. I have tried to clear the login sessions in login.aspx.cs, including Session["Login"] = null; and FormsAuthentication.SignOut(); but still nothing different.

<asp:LoginView runat="server" ViewStateMode="Disabled">
        <ul class="nav navbar-nav">
            <li><a runat="server" href="~/Info">Information</a></li>
        <ul class="nav navbar-nav navbar-right">
                <asp:LoginStatus runat="server" LogoutAction="Redirect" LogoutText="Log out" LogoutPageUrl="~/Login" OnLoggingOut="Unnamed_LoggingOut" />