Below, I have different variations of doing the same thing.  However, with each approach, after I update the text, I don't see the update occur within the actual Target segment object itself:

ISegmentPair activeSegmentPair = document.ActiveSegmentPair;

IAbstractMarkupData markupData = activeSegmentPair.Target.Find(IsIText); // IsItext is a function: bool IsItext(IAbstractMarkupData x) { return x is IText; }
IText targetText = markupData as IText;
if (targetText != null)
{
     targetText.Properties.Text = activeSourceText.ToString();
}

------------

ISegmentPair activeSegmentPair = document.ActiveSegmentPair;

document.ProcessSegmentPairs(
"Copy Source to Target",
(sp, args) =>
{
if (sp.Properties.Id.Id == activeSegmentPair.Properties.Id.Id)
{
     foreach (IAbstractMarkupData targetMarkupData in sp.Target)
     {
          var targetText = targetMarkupData as IText;
          if (targetText != null)
          {
               targetText.Properties.Text = activeSourceText.ToString();
          }
     }

}
);