If you change the value of an Asset's tag and that Asset already belongs in a Perspective Group, then when Perspectives are rebuilt that Asset will be re-grouped according to its new tag.
Once the Perspective has been updated, overnight processing will apply the new perspective to all reports. This means that the reports will reflect the Asset residing in the new Perspective Group (or Asset Not Allocated), including all historical months within the live report.
(Note: Changes to Asset Tags and Perspectives will not impact Archived reports)
This process is also the same if you're creating a new tag on an Asset - the Asset will be re-grouped according to its new tag.