Does my court paperwork need to specify the requirement for an IID and length of requirement?

If you were convicted of a first offense DUI AND you were convicted in a "pilot" county (Alameda, Los Angeles, Sacramento or Tulare) the court may not order the Ignition Interlock Device (IID), however, you will be required to install an IID by the Department of Motor Vehicles (DMV). Some Judges, in non-pilot counties will also order IID in certain circumstances. If you were convicted of a multiple offense (second DUI or more) you will need to install an IID if you want to shorten the suspension time required by the DMV, a judge may also make the IID a term of your probation. If you retained an attorney to help you defend your case they should be able to help you with the IID requirements, whether ordered by the court, or not. If you used the Public Defender as your lawyer, they usually do not know the interplay between the court conviction and the licensing ramifications at the DMV, however if you were ordered by the Judge to install an IID the Public Defender should be able to clarify the court order and how best to satisfy that order.

Then you probably are not required to do so, unless the court ordered it and forgot to put it in a written order.

Nope. IID is purely a DMV matter, and the court has no say whatsoever.