It is common in my experience for controllers to request that I advise of any change in altitude. Maybe I don't HAVE TO but it sure makes sense to comply with such a reasonable request in the interest of safety. I would think that course changes could be viewed similarly. The altitude consideration is especially true in or near terminal airspace which is, of course, where flight following is the most important. I have also had them say "resume own navigation" when they are able to do so.
Let's remember that requesting FF means we want assistance with separation. It only makes sense to make that assistance easier to give. Separation keeps the IFR traffic safer, too.