It appears that record updates/creates that are performed via API are not subject to triggers. Is this systemically true? And, is there a workaround to cause triggers to 'listen' for such activity?
What API do you mean?
REST
We are using it to create records, and also update them.
I can see from the code that REST runs triggers the same way UI does. I can check further if problem persists.
Server-side API which you can use in Object Script currently does not run triggers. Perhaps we should change this.
Does updating a field through REST API cause After Update triggers to execute? Recently it seems that the after update triggers are not executing where a couple weeks ago - they were..
Do you use "on field change" condition? There was a bug fix in REST API which may restore correct behavior.
If problem persists please submit support request so I could take a closer look.