Hi vereato,
You need to make ajax call in tree node click. Based on the selected value fetch the record from database and display.
Refer below example.
 Database
I have used the following table FamilyHierarchy with the schema as follows.

I have already inserted few records in the table.
The Parent of each Family Member can be determined using the ParentId column which stores the ParentId of the parent of a Member.

You can download the database table SQL by clicking the download link below.
Download SQL file
HTML
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script type="text/javascript" src="https://www.google.com/jsapi"></script>
<script type="text/javascript">
    google.load("visualization", "1", { packages: ["orgchart"] });
    google.setOnLoadCallback(drawChart);
    function drawChart() {
        $.ajax({
            type: "POST",
            url: "Default.aspx/GetChartData",
            data: '{}',
            contentType: "application/json; charset=utf-8",
            dataType: "json",
            success: function (r) {
                var data = new google.visualization.DataTable();
                data.addColumn('string', 'Entity');
                data.addColumn('string', 'ParentEntity');
                data.addColumn('string', 'ToolTip');
                for (var i = 0; i < r.d.length; i++) {
                    var memberId = r.d[i][0].toString();
                    var memberName = r.d[i][1];
                    var parentId = r.d[i][2] != null ? r.d[i][2].toString() : '';
                    data.addRows([[{
                        v: memberId,
                        f: memberName + '<div><img src = "Pictures/' + memberId + '.jpg" /></div>'
                    }, parentId, memberName]]);
                }
                var chart = new google.visualization.OrgChart($("#chart")[0]);
                chart.draw(data, { allowHtml: true });
                google.visualization.events.addListener(chart, 'select', function () {
                    $('#dvDetails').empty();
                    var selection = chart.getSelection();
                    if (selection.length > 0) {
                        var id = data.getValue(selection[0].row, 0);
                        $.ajax({
                            type: "POST",
                            url: "Default.aspx/GetDetails",
                            data: '{memberId:' + id + '}',
                            contentType: "application/json; charset=utf-8",
                            dataType: "json",
                            success: function (r) {
                                $('#dvDetails').append("<b>Name</b><br/>");
                                $.each(r.d, function (index, item) {
                                    $('#dvDetails').append(item[1] + "<br/>")
                                });
                            },
                            error: function (r) {
                                alert(r.responseText);
                            }
                        });
                    }
                });
            },
            error: function (r) {
                alert(r.responseText);
            }
        });
    }
</script>
<div id="chart">
</div>
<hr />
<div id="dvDetails"></div>
Namespaces
C#
using System.Data;
using System.Data.SqlClient;
using System.Configuration;
using System.Web.Services;
VB.Net
Imports System.Data
Imports System.Data.SqlClient
Imports System.Configuration
Imports System.Web.Services
Code
C#
[WebMethod]
public static List<object> GetChartData()
{
    List<object> chartData = new List<object>();
    string query = "SELECT MemberId, Name, ParentId FROM FamilyHierarchy";
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand(query))
        {
            cmd.CommandType = CommandType.Text;
            cmd.Connection = con;
            con.Open();
            using (SqlDataReader sdr = cmd.ExecuteReader())
            {
                while (sdr.Read())
                {
                    chartData.Add(new object[]
                    {
                        sdr["MemberId"], sdr["Name"], sdr["ParentId"]
                    });
                }
            }
            con.Close();
            return chartData;
        }
    }
}
[WebMethod]
public static List<object> GetDetails(int memberId)
{
    List<object> memberData = new List<object>();
    string query = "SELECT MemberId, Name, ParentId FROM FamilyHierarchy WHERE MemberId = @Id";
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand(query))
        {
            cmd.Parameters.AddWithValue("@Id", memberId);
            cmd.CommandType = CommandType.Text;
            cmd.Connection = con;
            con.Open();
            using (SqlDataReader sdr = cmd.ExecuteReader())
            {
                while (sdr.Read())
                {
                    memberData.Add(new object[]
                    {
                        sdr["MemberId"], sdr["Name"], sdr["ParentId"]
                    });
                }
            }
            con.Close();
            return memberData;
        }
    }
}
VB.Net
<WebMethod>
Public Shared Function GetChartData() As List(Of Object)
    Dim chartData As List(Of Object) = New List(Of Object)()
    Dim query As String = "SELECT MemberId, Name, ParentId FROM FamilyHierarchy"
    Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Using con As SqlConnection = New SqlConnection(constr)
        Using cmd As SqlCommand = New SqlCommand(query)
            cmd.CommandType = CommandType.Text
            cmd.Connection = con
            con.Open()
            Using sdr As SqlDataReader = cmd.ExecuteReader()
                While sdr.Read()
                    chartData.Add(New Object() {sdr("MemberId"), sdr("Name"), sdr("ParentId")})
                End While
            End Using
            con.Close()
            Return chartData
        End Using
    End Using
End Function
<WebMethod>
Public Shared Function GetDetails(ByVal memberId As Integer) As List(Of Object)
    Dim memberData As List(Of Object) = New List(Of Object)()
    Dim query As String = "SELECT MemberId, Name, ParentId FROM FamilyHierarchy WHERE MemberId = @Id"
    Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Using con As SqlConnection = New SqlConnection(constr)
        Using cmd As SqlCommand = New SqlCommand(query)
            cmd.Parameters.AddWithValue("@Id", memberId)
            cmd.CommandType = CommandType.Text
            cmd.Connection = con
            con.Open()
            Using sdr As SqlDataReader = cmd.ExecuteReader()
                While sdr.Read()
                    memberData.Add(New Object() {sdr("MemberId"), sdr("Name"), sdr("ParentId")})
                End While
            End Using
            con.Close()
            Return memberData
        End Using
    End Using
End Function
Screenshot
