When the ScreenPosition property of RadDesktopAlert is set to BottomRight in RightToLeft mode, it is shown in the center instead of in the right. Please refer to the attached sample project and attached screenshots.

Workaround:

 RadDesktopAlert rdAlert = new RadDesktopAlert();

 private void radButton1_Click(object sender, EventArgs e)
 {
     rdAlert.ContentText = "Sample text";
     rdAlert.ScreenPosition = AlertScreenPosition.BottomRight;
     rdAlert.ShowOptionsButton = false;
   
     rdAlert.FixedSize = new System.Drawing.Size(490, 135);
     rdAlert.Popup.LocationChanged += Popup_LocationChanged; 
     rdAlert.RightToLeft = System.Windows.Forms.RightToLeft.Yes;
     rdAlert.Show();
 }

 Point p = Point.Empty;

 private void Popup_LocationChanged(object sender, EventArgs e)
 {
     DesktopAlertPopup popup = sender as DesktopAlertPopup;
     if (p == Point.Empty)
     {
         p = popup.Location;
     }
     else
     { 
         rdAlert.Popup.LocationChanged -= Popup_LocationChanged;
         rdAlert.Popup.Location = p;
         rdAlert.Popup.LocationChanged += Popup_LocationChanged;
     }
 }