ASP.NET SQLDataSource SelectParameters not set correctly

I have an ASP.NET web form coded like this:

<asp:TextBox 
    ClientIDMode="Static"
    ID="_txtExitDate" 
    runat="server"
    EnableViewState="true" />

 <asp:TextBox 
    ClientIDMode="Static"
    ID="_txtEnterDate" 
    runat="server" 
    EnableViewState="true" />

<asp:Button
    runat="server" 
    ClientIDMode="Static" 
    ID="_btnSearch" 
    Text="Search" 
    OnClick="_btnSearch_Click" />

<asp:GridView
    ID="_gvRecords" 
    runat="server" 
    DataSourceID="_sdsRecords" 
    DataKeyNames="total_records"
    CellPadding="0"
    CellSpacing="0"
    ShowHeader="true"
    ShowFooter="true"
    PageSize="20"
    SelectedIndex="0"
    Width="100%"
    BorderStyle="None"
    GridLines="Horizontal"
    AutoGenerateColumns="false"
    AllowSorting="true" 
    AllowPaging="true" 
    EmptyDataText="No records." 
    OnPageIndexChanging="_gvRecords_PageIndexChanging"
    OnSorting="_gvRecords_Sorting" >
        <SelectedRowStyle CssClass="SelRow" />
        <HeaderStyle CssClass="GridHeader" />
        <AlternatingRowStyle CssClass="AltRow" BackColor="#F7F5E9" />
        <Columns>
            <asp:BoundField DataField="region" HeaderText="Region" SortExpression="region" />
            <asp:BoundField DataField="total_records" HeaderText="Records" SortExpression="total_records" />
        </Columns>
</asp:GridView>

Of course these are only the relevant tags the layout is managed by other code that's not important.

The form include a SQLDataSource defined like this:

<asp:SqlDataSource         
    runat="server"
    ConnectionString="<%$ ConnectionStrings:db %>"
    ProviderName="<%$ ConnectionStrings:db.ProviderName %>"
    ID="_sdsRecords"  
    OnSelecting="_sdsRecords_Selecting"
    SelectCommand ="
        SELECT
            COUNT(DISTINCT(records.id)) AS total_records,
            tab_cities.city_region AS region
        FROM
            records
                INNER JOIN
            tab_A ON records.id_subject = tab_A.id
                INNER JOIN
            tab_cities ON tab_cities.city_province_code = tab_A.province
        WHERE 
            (records.mode = 'S')
            AND (records.status = 'C')
            AND (records.delete_date IS NULL)
            AND (records.exit_date >= @exit)
            AND (records.enter_date <= @enter)
        GROUP BY
            tab_cities.city_region
        ORDER BY
            total_records DESC">
        <SelectParameters>
            <asp:Parameter Direction="Input" DbType="DateTime" Name="exit" />
            <asp:Parameter Direction="Input" DbType="DateTime" Name="enter" />
        </SelectParameters>
    </asp:SqlDataSource>

The codebehind is something like this:

protected void Page_Load(object sender, EventArgs e)
{
    if (!IsPostBack) {
        DateTime date = DateTime.Now;

        var firstDayOfMonth = new DateTime(date.Year, date.Month-1, 1);
        var lastDayOfMonth = firstDayOfMonth.AddMonths(1).AddDays(-1);

        _txtExitDate.Text = firstDayOfMonth.ToShortDateString();
        _txtEnterDate.Text = lastDayOfMonth.ToShortDateString();
    }
}

protected void _btnSearch_Click(object sender, EventArgs e)
{
    _sdsRecords.Select(DataSourceSelectArguments.Empty);
}

protected void _sdsNoleggi_Selecting(object sender, SqlDataSourceSelectingEventArgs e)
{
    DateTime _exit = DateTime.Parse(_txtExitDate.Text.Trim());
    DateTime _enter = DateTime.Parse(_txtEnterDate.Text.Trim());

    e.Command.Parameters["exit"].Value = _exit ;
    e.Command.Parameters["enter"].Value = _enter ;
}

The form seems to work at startup i.e. the query returns the number of rows I'm expecting but if I try to change the value of _txtExitDate and _txtEnterDate and click on search button nothing changes. _sdsNoleggi_Selecting() is triggered and command parameters are set correctly.

Another issue I cannot unserstand is why if I change <asp:Parameter /> with <asp:ControlParameter /> like this:

        <SelectParameters>
            <asp:ControlParameter DbType="DateTime" Name="exit" ControlID="_txtExitDate" PropertyName="Text" ConvertEmptyStringToNull="true" />
            <asp:ControlParameter DbType="DateTime" Name="enter" ControlID="_txtEnterDate" PropertyName="Text" ConvertEmptyStringToNull="true" />
        </SelectParameters>

parameters are not set correctly and then the whole query doesn't return any record (_sdsRecords_Selecting() event handler is removed in such case).

---- LATE UPDATE ----

As stated below the site this page come from is fully coded this way. Changing the paradigm of the whole thing is not an option.