Reading the "percentComplete" attribute is the correct way to do that. You can also read the "events" property of the Job object to get the history of updates.
I don't fully understand the problem you are having. What happens if you call the Job REST API before it reaches 91%? Does percentComplete jump from 0% to 91%? Could you please also indicate the "actionType" of the Job and the version of the Delphix Engine.