Word/SharePoint: permission change turns AutoSave off

Hi,

We have a SharePoint, to which users get access bases on access packages, where they collaborate mostly in Word docs.

We have the following issue:

• Users have Edit rights to the docs by default.
• When they open a Word document in Word desktop, and switch the permissions to Review, the AutoSave stays turned on.
• When another users changes the permissions to Review before sharing, the AutoSave is turned off when the user opens the doc in Word desktop.

My question is: is this supposed to work like this? If not, how could we possibly fix this?

When searching the community and other places, I cannot get a clear answer if it should work like this or not. Some write Review turns the AutoSave off, others say it should not.