[DXCategory("Action")]
public event TileViewBeforeItemDropEventHandler BeforeItemDrop

<DXCategory("Action")>
Public Event BeforeItemDrop As TileViewBeforeItemDropEventHandler

using DevExpress.XtraGrid;
using DevExpress.XtraGrid.Views.Tile;

private void TileView1_BeforeItemDrop(object sender, BeforeItemDropEventArgs e) {
    TileView view = sender as TileView;
    int newParentRowHandle = GetParentRowHandleFromGroupColumnValue(view, e.NewGroupColumnValue);
    if(view.IsValidRowHandle(newParentRowHandle)) {
        int tileAfterRowHandle = view.GetChildRowHandle(newParentRowHandle, e.TargetIndexInGroup);
        TaskRecord tileAfter = (TaskRecord)view.GetRow(tileAfterRowHandle);
        MessageBox.Show(tileAfter.Description);
    }
}
private int GetParentRowHandleFromGroupColumnValue(TileView view, object groupColumnValue) {
    // Iterates through the rows and looks for a row that matches the group column value.
    // Returns the row's parent row handle.
    for(int rowHandle = 0; rowHandle < view.DataRowCount; rowHandle++) {
        TaskRecord row = (TaskRecord)view.GetRow(rowHandle);
        if (row.Status.Equals(groupColumnValue)) {
            int parentRowHandle = view.GetParentRowHandle(rowHandle);

            if (view.IsGroupRow(parentRowHandle))
                return parentRowHandle;
        }
    }
    return GridControl.InvalidRowHandle;
}

// ...
public enum TaskStatus { ToDo, Planned, Doing, Testing, Done }
public class TaskRecord {
    public string Caption { get; set; }
    public string Description { get; set; }
    public Image AttachedImage { get; set; }
    public TaskStatus Status { get; set; }
}

Imports DevExpress.XtraGrid
Imports DevExpress.XtraGrid.Views.Tile

Private Sub TileView1_BeforeItemDrop(ByVal sender As Object, ByVal e As BeforeItemDropEventArgs)
    Dim view As TileView = TryCast(sender, TileView)
    Dim newParentRowHandle As Integer = GetParentRowHandleFromGroupColumnValue(view, e.NewGroupColumnValue)
    If view.IsValidRowHandle(newParentRowHandle) Then
        Dim tileAfterRowHandle As Integer = view.GetChildRowHandle(newParentRowHandle, e.TargetIndexInGroup)
        Dim tileAfter As TaskRecord = CType(view.GetRow(tileAfterRowHandle), TaskRecord)
        MessageBox.Show(tileAfter.Description)
    End If
End Sub
Private Function GetParentRowHandleFromGroupColumnValue(ByVal view As TileView, ByVal groupColumnValue As Object) As Integer
    ' Iterates through the rows and looks for a row that matches the group column value.
    ' Returns the row's parent row handle.
    For rowHandle As Integer = 0 To view.DataRowCount - 1
        Dim row As TaskRecord = CType(view.GetRow(rowHandle), TaskRecord)
        If row.Status.Equals(groupColumnValue) Then
            Dim parentRowHandle As Integer = view.GetParentRowHandle(rowHandle)

            If view.IsGroupRow(parentRowHandle) Then
                Return parentRowHandle
            End If
        End If
    Next rowHandle
    Return GridControl.InvalidRowHandle
End Function

' ...
Public Enum TaskStatus
    ToDo
    Planned
    Doing
    Testing
    Done
End Enum
Public Class TaskRecord
    Public Property Caption() As String
    Public Property Description() As String
    Public Property AttachedImage() As Image
    Public Property Status() As TaskStatus
End Class

tileView1.BeforeItemDrop += TileView1_BeforeItemDrop;
}

gridControl1.DataSource = DataHelper.GetData()
    AddHandler tileView1.BeforeItemDrop, AddressOf TileView1_BeforeItemDrop
End Sub