https://www.bbc.co.uk/news/uk-scotland-65411666
What the BBC says in that article is that "it was agreed" that the stone would return to Westminster at such times. Important to realise that it was not agreed, however, with the people of Scotland but with the British crown, the stone having been stolen by the English king Edward I
BBC NewsStone of Destiny heads south for coronationThe ancient symbol of Scotland's monarchy leaves Edinburgh Castle on its way to London for the Coronation.