Secondary work permit - do I need to inform the NIA?

Hi all, I recently received a secondary work permit for working 8hrs at a different school to my primary sponsor. I was just at the NIA in Taipei city with my documents to update my ARC info and was told I don’t need to inform the NIA if the job is parttime. Has anyone had a similar experience? I would have thought they would need to know I am legal at the second school in case of raids, etc.