It is easy to shift a TIN vertically. Use Triangulation File Utilities (TINUTIL). Make a backup copy of you TIN file first.
Run the command,
Load the TIN from file,
Hit the Add button to add a value to the TIN elevations.
Save the shifted TIN over the original.
The contours need to be regenerated since both the elevation and position generally change.
You can contour from the shifted TIN with the command CNTRTIN or if the surface is in the Surface Manager the contours should be regenerated automatically.