Have a user utilizing one of our API products to insert new records and update existing ones. A workflow has been created on the user account that should auto-fire when any record is inserted or updated. However, said flow is never fired.

I looked at the docs and saw that there is the ability to trigger a flow from the REST API, but I assumed this would be taken care of automatically since the flow itself is triggered from a record change. The issue is that the flow itself is just never being run, including the check, which dictates how data is changed. Is there something I am missing here? They say that the same workflow can be kicked off from the Dataloader when creating new records. Am I missing a toggle with the REST API?