As far as I know there are no standard rules for this - although you may find some airports have AIP entries with local procedures.
Whether a controller wants to know about airborne or runway vacated will depend on a lot of things. For example if something else depends on knowing that the runway is no longer occupied, say, to give the next inbound a landing clearance. It will also depend on what type of equipment there is available to the controller - a good 'Advanced-Surface Movement Guidance and Control System, A-SMGCS, will normally tell the controller everything he or she needs to know.
Then there are individual controller preferences - some ask for such a report simply for confrmation that your day is not going horribly wrong!