I found an example on line with source code that was written with Infreagistics 6.3 version. That example did just what I needed. The example provided a handler the UtlraTree's MouseEnter event and the use of the  UltraTooTipManger to determine whether a tooltip was displayed or not. Listed below is the example MouseEnter event handler from the example. I modified the example to fit my own requirements.

 private void ultraTree1_MouseEnterElement(object sender, Infragistics.Win.UIElementEventArgs e)
{
 if (e.Element is Infragistics.Win.UltraWinTree.NodeTextUIElement)
 {
  // Get the location of the cursor
  Point pt = new Point(e.Element.Rect.X,e.Element.Rect.Y);
  Infragistics.Win.UltraWinTree.UltraTreeNode node = this.ultraTree1.GetNodeFromPoint(pt);
    
  // If the cursor is on a Tree node
  if (node != null)
  {
   Infragistics.Win.UltraWinToolTip.UltraToolTipInfo tipInfo = new Infragistics.Win.UltraWinToolTip.UltraToolTipInfo(node.Text,Infragistics.Win.ToolTipImage.Default, "", Infragistics.Win.DefaultableBoolean.True);
     this.ultraToolTipManager1.SetUltraToolTip(this.ultraTree1, tipInfo);
     this.ultraToolTipManager1.ShowToolTip(this.ultraTree1);
  }
 }
 else
  this.ultraToolTipManager1.HideToolTip();
}