I reckon the clue is in:
(iii) instructor time should be recorded as appropriate and also entered as PIC.
You're on board for a reason, so you're acting as an instructor instead of just a passenger. As it's an integrated program the student does not have a licence yet, so that's another reason for you to be PIC. One way to remember is that ALL flights during which you are acting in your instructor capacity are logged as both instructor time and PIC by you. Whether the student logs something as dual or as SPIC is up to the syllabus, the format of the course and the outcome of the flight. If you have to intervene in the process at any time during the flight, if you have to take over control for example, the flight cannot be logged as SPIC anymore and should revert to being a regular 'dual' flight for the student. In such a case the flight needs to be redone and if the outcome is up to standards, the student can then log this as originally intended. None of this changes what you log on your end.
The OPS manual should make this clear and if that is not the case, it could be the start of an interesting conversation about procedures at your ATO
