Hi Peter,
Yes, you are correct the APOKZ field gets set indirectly during activation of integration model. The above configuration settings as far as I am aware of "Immediate transfer", will also work if the integration model is active. We also had similar issues and when we tried debugging the code, we understood that in BD52 (change pointers transaction) if you check for material masters there are a list of tables and fields whose changes gets captured in this. Only when a value related to those fields are changed then the change pointer is captured and it checks this configuration settings and it updates the products in APO. Due to some reason although we had the custom field inserted in this selection, the APOKZ field was not getting flagged (even though the IM was active). This used to happen for some custom fields and not all. If you check in BD52 for MARC table you will also find the field APOKZ in it.
Due to this we came to a conclusion about the relevance of APOKZ field not getting set for some custom fields although there was an active integration model for data transfer of materials with the immediate transfer.
Hope I have provided my understanding correctly.
Regards
Sasi